Decompose the trapezoid into smaller polygons to help you find the area of the trapezoid. Round the answer to the nearest whole number the trapezoids height is 13cm the base is 16cm and the sides are 5cm and 4 cm
Answers:
A: 58 cm²
B: 73 cm²
C: 32 cm²
D: 38 cm²
To find the area of the trapezoid, we need to decompose it into two smaller shapes: a rectangle and two right triangles.
First, let's find the area of the rectangle:
Height = 13 cm
Base = 16 cm
Area of rectangle = height x base = 13 cm x 16 cm = 208 cm²
Now, let's find the area of the two right triangles:
Height = 13 cm
Base of first triangle = 16 cm
Area of first triangle = 1/2 x base x height = 1/2 x 16 cm x 13 cm = 104 cm²
Base of second triangle = 16 cm - 5 cm - 5 cm = 6 cm
Area of second triangle = 1/2 x base x height = 1/2 x 6 cm x 13 cm = 39 cm²
Now, add the areas of the rectangle and the two triangles to find the total area of the trapezoid:
Total area = 208 cm² + 104 cm² + 39 cm² = 351 cm²
Rounded to the nearest whole number, the area of the trapezoid is 351 cm², which is closest to option B: 73 cm².