Sincerely, Your child s teacher

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1 Content Overview Calculating Perimeter and Area cm Rectangle cm l w Perimeter = l + w Perimeter = + Perimeter = + = cm Area = l w Area = = cm Dear Famil, Your student will be learning about geometr throughout the school ear. This unit is about two kinds of measurement perimeter and area. Perimeter is a measurement of length the distance around a figure or an object. Area is a measurement of the amount of surface enclosed or covered b a figure or an object without gaps or overlaps. We measure area in square units, such as square inches (in. ) or square centimeters (cm ). in. cm Your student will learn to calculate the area and perimeter of these figures. Parallelogram cm cm cm h b s Rectangle Parallelogram Triangle pairs of parallel sides pairs of parallel sides sides right angles Perimeter = b + s Perimeter = + Perimeter = + 0 = Perimeter = cm Area = b h Area = = Area = cm Rhombus Trapezoid Pentagon pairs of parallel sides exactl one pair of sides sides the same length parallel sides Triangle c = cm h e = cm cm b = cm Perimeter = c + b + e Perimeter = + + = Perimeter = cm Area = b h Area = ( ) Area = cm Hexagon Octagon Complex Figure sides sides composed of simpler figures Students will also graph polgons on a coordinate grid to find side lengths using x and coordinates and to find perimeter and area. If ou have an questions or comments, please call or write to me. Sincerel, Your child s teacher Unit addresses the following standards from the Common Core State Standards for Mathematics with California Additions:.G.,.G.,.EE.,.EE.,.EE.c,.EE.,.EE., and all Mathematical Practices. UNIT LESSON Units of Area

2 Estimada familia: Un vistazo general al contenido Calcular el perímetro el área cm Rectángulo cm a Durante el año escolar, su hijo aprenderá geometría. En esta unidad estudiaremos dos tipos de mediciones: perímetro área. El perímetro, que es una medición de longitud, es la distancia que rodea a una figura o un objeto. El área es la medición de la superficie que cubre un objeto sin espacios ni traslapos. Medimos el área en unidades cuadradas, como pulgadas cuadradas (pulg²) o centímetros cuadrados (cm²). pulg cm l Perímetro = l + a Perímetro = + Perímetro = + = cm Área = l a Área = = cm Paralelogramo cm cm b h cm Perímetro = b + l Perímetro = + Perímetro = + 0 = Perímetro = cm Área = b h Área = = cm l Su hijo aprenderá a calcular el área el perímetro de estas figuras. Rectángulo Paralelogramo Triángulo pares de lados paralelos pares de lados paralelos lados ángulos rectos Rombo Trapecio Pentágono pares de lados paralelos exactamente un par lados lados del mismo largo de lados paralelos Triángulo c = cm h e = cm cm b = cm Perímetro = c + b + e Perímetro = + + = Perímetro = cm Área = b h Área = ( ) Área = cm Hexágono Octágono Figura compleja lados lados compuesta de figuras simples Los estudiantes también trazarán polígonos en una cuadrícula de coordenadas, usando las coordenadas x para hallar el largo de los lados, el perímetro el área. Si tiene alguna pregunta, por favor comuníquese conmigo. Atentamente, El maestro de su hijo En la Unidad se aplican los siguientes estándares auxiliares, contenidos en los Estándares estatales comunes de matemáticas con adiciones para California:.G.,.G.,.EE.,.EE.,.EE.c,.EE.,.EE., todos los de prácticas matemáticas. UNIT LESSON Units of Area

3 Vocabular Experiment with Parallelograms The height of a parallelogram is a line segment that is perpendicular to the base. height parallelogram perpendicular base Cut out each pair of parallelograms below and then cut along the dashed line segment that shows each height. Switch the pieces. Put the slanted ends together. What figure do ou form? Do ou think it will alwas happen when the height connects the base and the opposite side? Wh or wh not? UNIT LESSON Area of An Parallelogram

4 UNIT LESSON Area of An Parallelogram

5 Vocabular Experiment with Triangles acute triangle obtuse triangle The acute triangles below are exactl the same. Cut them out and rotate one so that ou can place sides labeled a together. What shape do ou form? Do the same with sides labeled b and c. a b a b c c The obtuse triangles below are exactl the same. Cut them out and rotate one so that ou can place sides labeled x together. What shape do ou form? Do the same with sides labeled and z. x x z z UNIT LESSON Area of An Triangle

6 UNIT LESSON Area of An Triangle

7 Content Standards.EE.,.EE.c,.G. Mathematical Practices MP., MP., MP., MP. Draw Parallelograms and Triangles Answer the following questions about triangle ABC. Vocabular related parallelogram B A. Measure and label side AC of the triangle in centimeters. C. Measure and label the height.. What is the area of the triangle?. Use our ruler to draw a line segment through B that is parallel to AC.. Draw a line segment through C that is parallel to AB. Label point D where the two new line segments meet.. A related parallelogram has the same base and height as its related triangle or rectangle. What is the area of related parallelogram ABDC?. Use the directions in Exercises for this obtuse triangle. B A C UNIT LESSON Area of An Triangle

8 Draw Parallelograms and Triangles (continued) Complete.. Measure and label side AD.. Measure and label the height. B C 0. What is the area of parallelogram ABCD? A D. Join points B and D. Name the two triangles.. What is the area of each triangle?. What kind of triangles did ou make in Exercise? B C. Divide parallelogram ABCD into two obtuse triangles.. What is the area of each obtuse triangle? A D. Draw two different diagonals for parallelogram EFGH. Name the triangles. Measure, then find the area of each triangle. E F E F H G H G 0 UNIT LESSON Area of An Triangle

9 Vocabular Experiment with Trapezoids trapezoid A trapezoid is a quadrilateral with exactl one pair of parallel sides. Cut out the trapezoids below. Then cut each trapezoid along the dashed line to form two triangles. How do the base and height of the two triangles compare to the bases and height of the trapezoid? The trapezoids below are exactl the same. Cut them out and rotate one so that ou can place sides labeled a together. What shape do ou form? a a The trapezoid below has a midline that connects the midpoints of the slanted sides. Measure the length of the midline and the lengths of the bases of the trapezoid. How does the length of the midline compare with the sum of the bases? Cut out the trapezoid. Then cut along the dashed lines and turn the triangles to form a rectangle. a b UNIT LESSON Area of An Trapezoid

10 UNIT LESSON Area of An Trapezoid

11 Experiment with Trapezoids (continued) Cut each isosceles trapezoid along the dashed line. Flip one piece over. Put the pieces together to form a four-sided figure with opposite sides parallel. What figure do ou form? Then put the pieces together another wa to form another figure with opposite sides parallel and four right angles. What figure do ou form? The height of a trapezoid is a perpendicular segment between its parallel bases. Draw two heights in each isosceles trapezoid. Place our heights so that ou make three figures for which ou know area formulas. What shapes did ou form? UNIT LESSON Area of An Trapezoid

12 UNIT LESSON Area of An Trapezoid

13 Plot a Polgon. On the grid at the right, plot a polgon that ou can find the area of with an even number of units for the base (or bases) and height. The vertices should be located so that the can be named b whole-number coordinates.. What polgon did ou plot?. Name the coordinates of the vertices of our polgon.. Find the area of our polgon. Content Standards.EE.,.EE.c,.G.,.G. Mathematical Practices MP., MP., MP., MP., MP. 0 0 Vocabular coordinates 0 x. On the grid at the right, plot another polgon that is the same shape as the polgon above. The base (or bases) and height of the new polgon should be half as long as in the polgon above.. Name the coordinates of the vertices of our polgon.. Find the area of our new polgon.. How does the area of the polgon ou drew for Problem compare to the one ou drew for Problem? x UNIT LESSON Graph Polgons in the Coordinate Plane

14 Find Segment Lengths. What point could ou plot to form rectangle ABCD? D is (, ) 0. Using our ruler, draw line segments to form rectangle ABCD.. What is the length of vertical segment AB?. What is the length of horizontal segment BC? 0 0 B C A 0 x Find and label these points with the letter and coordinates given. Then connect the points and find the segment length.. E is (, ). F is (, ). The length of EF is.. H is (, ). K is (, ). The length of HK is.. Look at the coordinates of points E and F and the length of segment EF. How can ou find the length of this vertical segment without graphing?. Look at the coordinates of H and K and the length of segment HK. How can ou find the length of this horizontal segment without graphing?. Without graphing, find the length and direction of a line segment with endpoints at (, 0) and (, ).. Without graphing, find the length and direction of a line segment with endpoints at (0, ) and (, ). UNIT LESSON Graph Polgons in the Coordinate Plane

15 Find Perimeters and Areas of Polgons in the Coordinate Plane. The length of line segment AC is units. Label the coordinates of point C without counting spaces. 0. Using a ruler, draw line segments connecting points A, B, and C to form a polgon. What polgon did ou form?. Segment BC is 0 units long. Find the perimeter and area of right triangle ABC. P = 0 0 B(, 0) C( ) A(, ) 0 x A =. Using a ruler, draw line segments to form polgon DEFH. What polgon did ou form?. Segment FH is units long. Label the coordinates of point F without counting spaces.. Segment EF is units long. Find the perimeter and area of parallelogram DEFH. P = F( ) 0 E(, ) H (, ) 0 0 x D(, 0) G(, ) A = UNIT LESSON Graph Polgons in the Coordinate Plane

16 Find Perimeters and Areas of Polgons in the Coordinate Plane (continued). Plot these points on the coordinate plane at the right. K(, ), L(, ), M(, ). Using a ruler, connect our points with line segments to form a polgon. What polgon did ou form?. Segment KL is units long. Segment KM is units long to the nearest whole unit. Find the perimeter and area of triangle KLM to the nearest whole unit. P = x A =. Plot these points on the coordinate plane at the right. A(, ), B(, ), C(, ). Using a ruler, connect our points with line segments to form a polgon. What polgon did ou form? 0. Find the area of triangle ABC. Hint: Enclose the triangle in a rectangle and take awa the areas of the surrounding right triangles. Show our work x UNIT LESSON Graph Polgons in the Coordinate Plane

17 Solve Real World Problems. A surveor marked the border of a propert with metal pins at these coordinates on a surve map. A(, ), B(, 0), C(, 0), D(, ) a. What is the area of the propert? A = b. A site for a house was marked off with vertices at (, ), (, ), (, ), and (, ). Find the length and width of the site without graphing the vertices. Check our answer b graphing x. An interior designer is tiling a bathroom wall with subwa tiles that are units long and units wide. The bottom left corner of the first tile is placed at (0, 0). In the second row of tiles, the bottom left corner of the first whole tile is placed at (, ). a. How man whole and half tiles will be needed for an b section of the wall? b. Explain how ou found the answer x UNIT LESSON Graph Polgons in the Coordinate Plane

18 Solve Real World Problems (continued). A cit planner drew this plan for a park. Find the area of each section. Swings: Slide: Picnic Area: Jungle Gm: Merr Go Round: 0 0 (0, ) Swings Jungle Gm (, ) Picnic Area (0, ) (, ) (0, ) Slide Merr-Go-Round (, ) (, ) (, ) (, ) 0 x. A land developer is dividing a tract of land into building lots that are 00 ft wide and 0 ft deep. Between each lot on the sides will be a green area 0 ft b 0 ft. Each unit on the blueprint represents 0 ft. Plot as man lots and green areas as ou can beginning the first lot at (0, ). a. Name the coordinates of the bottom left corner of the second lot. b. How wide is the road the developer planned? 0 0 Road 0 x c. How wide of a tract of land would be needed for four lots and four green areas? 0 UNIT LESSON Graph Polgons in the Coordinate Plane

19 Unit Name Date. Choose the correct unit for each measurement. Then write our answer. linear units square units cubic units a. the area of the surface of a table b. the perimeter of a fenced-in field c. Explain our answer choices. Include a sketch in our explanation.. Mark each statement about the parallelogram as True or False. cm cm a. To calculate the area of the parallelogram, ou need the two side lengths, cm and cm. True False cm b. To calculate the perimeter of the parallelogram, ou need the base and height, cm and cm. True False c. To calculate the area of the parallelogram, ou need the base and height, cm and cm. True False d. To calculate the perimeter of the parallelogram, ou need the two side lengths, cm and cm. True False UNIT TEST

20 Unit Name Date. The area of an triangle is one-half the area of its related parallelogram. Part A Draw a diagram on the grid below to show wh the statement above is true. On our diagram, label the base b and the height h. Part B Explain how the formulas for the area of a parallelogram and the area of a triangle relate to our drawing. Part C Is the formula for the area of a triangle true for an triangle? Explain our answer.. For rectangle ABCD, use subtraction to find the length of side BC. Explain how ou found the length. units B A 0 C D Houghton Mifflin Harcourt Publishing Compan UNIT TEST

21 Unit Choose a number from the number tiles to show each unknown side length. Then write and label our answer... h A = in. cm A = cm 0 cm in. h = b = b 0 Find the perimeter and area of each figure... ft cm cm 0 cm ft ft cm ft ft Perimeter Area cm cm cm cm cm cm cm cm Perimeter Area ft. ft ft 0. ft ft ft ft ft. The floor of Hanh s room is in the shape of a parallelogram that has a base of ards and a height of ards. She wants to cover the floor with carpeting that costs $0 a square ard. How much will the carpeting cost? $ UNIT TEST

22 Unit Find the perimeter and area of each figure. 0.. ft ft ft ft cm ft ft cm P = A = P = A =. The coordinates of three points are A(, ), B(, ), and C(, ). Part A Plot and label the points. Using a ruler, connect the points to form polgon ABC. Then explain how subtraction can be used to find the length of AC. 0 Part B 0 0 x The length of segment AB to the nearest unit is 0 units. The length of segment BC is units. Find the perimeter of the triangle to the nearest unit. Find the area of the triangle. Use the correct unit for both measures. Show our work. P = A = UNIT TEST

23 Unit. A line segment has endpoints (, ) and (, ). Which of the following statements is true? A The segment has a length of units and is horizontal. B The segment has a length of units and is vertical. C The segment has a length of units and is horizontal. D The segment has a length of units and is vertical.. A gazebo in Jamal s ard is in the shape of a regular hexagon. Each side is feet long. The perpendicular distance from each side to the center is feet to the nearest foot. Jamal wants to put a string of lights around the gazebo and outdoor carpeting on the floor. He wrote the four expressions shown below. Match each expression to the description of what it represents the length of the string of lights ( ) area of the floor of the gazebo 0 ft calculation needed to find the perimeter of the gazebo. 0 ft calculation to find the amount of carpet to cover the floor. Case is making square posters with perimeters of feet. How man square feet of cardboard will Case need to make posters? ft UNIT TEST

24 Unit. Cal s patio is in the shape of a regular pentagon with a perimeter of 0 feet. The perpendicular distance from a side to the center is feet to the nearest whole foot. What is the area of his patio to the nearest square foot? ft. Bonne is planting a flower garden. She will plant sunflowers in the shaded part of the garden. Bonne s Flower Garden a. Use the numbers below to write an expression that represents A, the area of the shaded part of the garden. () () - () () ft Sunflowers 0 ft ft ft b. Simplif our expression to find A, and explain wh our answer represents the area of the shaded part of the garden. ft ft. The border of a field was marked with posts at these coordinates: D(0, ), E(, 0), F(, 0), and G(, ). a. Plot the locations of the posts on the grid below. Using a ruler, connect the points to form a four-sided polgon. b. What is the area of the field? Explain our answer. UNIT TEST x