Section 10 1 Area of Parallelogram and Triangles

Section 10: 1 Area of Parallelogram and Triangles GEOMETRY ROGER CARESIA

Perimeter and Area of a Parallelogram Find the perimeter and area of Perimeter Since opposite sides of a parallelogram are congruent, RS UT and RU ST. So UT = 32 in. and ST = 20 in.

Perimeter and Area of a Parallelogram Perimeter = RS + ST + UT + RU = 32 + 20 + 32 + 20 Area = 104 in. Find the height of the parallelogram. The height forms a right triangle with points S and T with base 12 in. and hypotenuse 20 in. c 2 = a 2 + b 2 Pythagorean Theorem 202 = 122 + b 2 c = 20 and a = 12 400 = 144 + b 2 Simplify.

Perimeter and Area of a Parallelogram 256 = b 2 Subtract 144 from each side. 16 = b Take the positive square root of each side. The height is 16 in. UT is the base, which measures 32 in. A = bh = (32)(16) or 512 in 2 Area of parallelogram b = 32 and h = 16 Answer: The perimeter is 104 in. and the area is 512 in 2.

Find the perimeter and area of A. 88 m; 255 m 2 B. 88 m; 405 m 2 C. 88 m; 459 m 2 D. 96 m; 459 m 2

Area of a Parallelogram Find the area of Step 1 Use a 45°-90° triangle to find the height h of the parallelogram.

Area of a Parallelogram Recall that if the measure of the leg opposite the 45° angle is h, then the measure of the hypotenuse is Substitute 9 for the measure of the hypotenuse. Divide each side by .

Area of a Parallelogram Step 2 Find the area. A = bh Area of a parallelogram. Multiply. Answer: 76. 4 square units

Find the area of A. 156 cm 2 B. 135. 76 cm 2 C. 192 cm 2 D. 271. 53 cm 2

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?

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 = 7. 1

Perimeter and Area of a Triangle Step 3 Use unit analysis to determine how many of each item are needed. Boards boards Bags of Sand

Perimeter and Area of a Triangle Round the number of boards up so there is enough wood. Answer You will need 12 boards and 5 bags of sand.

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

Perimeter and Area on the Coordinate Plane Find the perimeter and area of △ABC with vertices A(4, – 2), B(12, 6), and C(– 4, 6). Step 1 Find the perimeter of ∆ABC. Use the distance formula to find the length of each side.

Perimeter and Area on the Coordinate Plane

Perimeter and Area on the Coordinate Plane The perimeter of △ABC is or about 38. 6 units. Step 2 Find the area of ∆ABC. Using as the base, the height is the perpendicular distance from A to From the graph the height is 8 units.

Perimeter and Area on the Coordinate Plane Area of a triangle. Substitute and simplify. The area of ∆ABC is 64 square units. Answer: or about 38. 6 units; 64 units 2

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