Ch 10. 4 10: 18 = 5: 9 2(2) + 4(2) + 5(2) = 22 meters JK = KL 15 = KL WX XY 9 6 6_ = x_ 2. 5 35 KL = 10 x = 84 5_ = 8_ x+3 2 x x = 12
Ch 10. 4 Areas of Triangles Learning Target: I will be able to find the areas of triangles. Standard 10. 0 Students compute areas of polygons, including scalene triangles and equilateral triangles.
Ch 10. 4 Theorem 10 -3
Ch 10. 4 Perimeter and Area of a Triangle SANDBOX You need to buy enough boards to make the frame of the triangular sandbox shown and enough sand to fill it. If one board is 3 feet long and one bag of sand fills 9 square feet of the sandbox, how many boards and bags do you need to buy?
Ch 10. 4 Perimeter and Area of a Triangle Step 1 Find the perimeter of the sandbox. Perimeter = 16 + 12 + 7. 5 or 35. 5 ft Step 2 Find the area of the sandbox. Area of a triangle b = 12 and h = 9
Ch 10. 4 Perimeter and Area of a Triangle Step 3 Use unit analysis to determine how many of each item are needed. Boards boards round up to 12 boards Bags of Sand
Ch 10. 4 PLAYGROUND You need to buy enough boards to make the frame of the triangular playground shown here and enough mulch to fill it. If one board is 4 feet long and one bag of mulch covers 7 square feet, how many boards and bags do you need to buy? A. 12 boards and 14 bags of mulch B. 11 boards and 13 bags of mulch C. 12 boards and 13 bags of mulch D. 11 boards and 14 bags of mulch
Ch 10. 4 Use Area to Find Missing Measures ALGEBRA The height of a triangle is 7 inches more than its base. The area of the triangle is 60 square inches. Find the base and height. Step 1 Write an expression to represent each measure. Let b represent the base of the triangle. Then the height is b + 7. Step 2 Use the formula for the area of a triangle to find b. Area of a triangle
Ch 10. 4 Use Area to Find Missing Measures Substitution 120 = (b)(b + 7) Multiply each side by 2. 120 = b 2 + 7 b Distributive Property Subtract 120 from each side. Factor. Zero Product Property Solve for b. 0 = b 2 + 7 b – 120 0 = (b – 8)(b + 15) b – 8 = 0 and b + 15 = 0 b=8 b = – 15
Ch 10. 4 Use Area to Find Missing Measures Step 3 Use the expressions from Step 1 to find each measure. Since a length cannot be negative, the base measures 8 inches and the height measures 8 + 7 or 15 inches. Answer: b = 8 in. , h = 15 in.
Ch 10. 4 ALGEBRA The height of a triangle is 12 inches more than its base. The area of the triangle is 560 square inches. Find the base and the height. A. base = 56 in. and height = 10 in. B. base = 28 in. and height = 40 in. C. base = 20 in. and height = 56 in. D. base = 26 in. and height = 38 in.