11.1 areas of parallelograms and triangles 2016 ink.noteook Page 126 Page 128 Page 127 11.1 Area of Parallelograms and Triangles Lesson Ojectives Standards Lesson Notes Page 129 11.1 Areas of Parallelograms and Triangles Press the tas to view details. 1
d2 d2 d1 d1 11.1 areas of parallelograms and triangles 2016 ink.noteook Lesson Ojectives Standards Lesson Notes Lesson Ojectives Standards Lesson Notes After this lesson, you should e ale to successfully find the area of a parallelogram and a triangle. You will also use the area to find missing lengths. G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. G.MG.1 Use geometric shapes, their measures, and their properties to descrie ojects. G.MG.3 Apply geometric methods to solve design prolems. Press the tas to view details. AREA OF A SQUARE: s A = s 2 The area of a square is the square of the length of its side. Area Figure Formula Rectangle h A = h AREA OF A RECTANGLE h A = h AREA OF A PARALLELOGRAM h A = h AREA OF A TRIANGLE h or The area of a rectangle is the product of its ase and height. (or you can use A = w) The area of a parallelogram is the product of a ase and its corresponding height. Base of a parallelogram either pair of parallel sides of a parallelogram are ases. Height of a parallelogram: the perpendiculardistance etween any two parallel ases. The area of a triangle is one half the product of a ase and its corresponding height. Like a parallelogram, the ase can e any side, and the height is the length of an altitude drawn to a given ase Square s A = s 2 Parallelogram h A = h Triangle Rhomus Kite h h A = 2 h Trapezoid 1 A= h(1 + 2) 2 Circle 1 2 r A = πr 2 C = 2πr 2
11.1 areas of parallelograms and triangles 2016 ink.noteook 1. 2. 3. 4. 5. A athroom tile floor is made of lack and white parallelograms. Each parallelogram is made of two triangles with dimensions as shown. Find the perimeter and area of one parallelogram. 3
6. The height of a parallelogram is 5 feet more than its ase. If the area of the parallelogram is 204 square feet, find its ase and height. ase = height = 7. 8. 9. 10. 4
11.1 areas of parallelograms and triangles 2016 ink.noteook 11. 12. 13. The ase of a triangle is one half of its height. If the area of the triangle is 36 square millimeters, find its ase and height. ase = height = 5
On the Worksheet HOMEWORK Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 1. 2. 11.1 Practice on Areas of Parallelograms and Triangles 6
Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 3. 4. Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 5. 6. Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 7. 8. Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 9. 10. 7
11. A ox with a square opening is squashing into the rhomus shown elow. What is the area of the opening? 12. The height of a parallelogram is 10 feet more than its ase. If the area of the parallelogram is 120 square feet, find its ase and height. 13. The ase of a triangle is one half of its height. If the area of the triangle is 196 square millimeters, find its ase and height. 14. The height of a parallelogram is three times its ase. If the area of the parallelogram is 972 square inches, find its ase and height. 8
15. The ase of a triangle is four times its height. If the area of the triangle is 242 square millimeters, find its ase and height. 16. FRAMING A rectangular poster measures 42 inches y 26 inches. A frame shop fitted the poster with an additional halfinch mat order. a) Find the area of the poster. ) Find the area of the mat order. c) Suppose the wall is marked where the poster will hang. The marked area includes an additional 12 inch space around the poster and frame. Find the total wall area that has een marked for the poster. 17. A square and a rectangle have equal area. If the rectangle is 36 cm y 25 cm, what is the perimeter of the square? a) 30 cm ) 60 cm c) 120 cm d) 900 cm 18. What is the area in square units of a rectangle with vertices ( 2, 5), (3, 5), (3, 1), and ( 2, 1)? y x 9
Answers: Answers: 1. P = 64.1 mm, A = 108 mm 2 3. P = 96 in, A = 404.5 in 2 5. P = 55 km, A = 166.5 km 2 7. P = 58.0 in, A = 144.5 in 2 9. P = 36 cm, A = 56.6 cm 2 11. A = 98 in 2 13. h = 28 m, = 14 m 14. = 18 in, h = 54 in 17. C 10