Question

A trapezoid has two right angles and bases that measure 16m and 8m. The right triangle formed by an altitude has a hypotenuse of 4 square root 5m. Sketch the trapezoid. What are its perimeter and area?

Answer 1

The trapezoid would that would be formed from the description would have a rectangle and a triangle. The shorter base of the trapezoid would be the length of the rectangle while the longer base would be the sum of the length of the rectangle and the base of the triangle. So, the dimensions would be:

length of the rectangle = 8 m
base of triangle = 16 - 8 = 8 m
hypotenuse = 4√5 m

width of the rectangle = √(4√5 - 8) = 4 m

Perimeter = 8 + 16 + 4√5 + 4 = 28 + 4√5 m
Area = area of triangle + area of rectangle
Area = 8(4) / 2 + 8(4) = 48 m^2