Question

A trapezoid has base lengths of 12 centimeters and 13 centimeters. The other sides have lengths of 5 centimeters and 10 centimeters. A rectangle with side lengths of 2 centimeters and 5 centimeters is connected to the side with length 10 centimeters.
What is the area of the composite figure?

70 cm2
100 cm2
105 cm2
130 cm2

Answer 1

The distance (height) between the two bases is at most the shorter of the nonparallel sides, i.e. ≤ 5. So the trapezoid’s area is

(12 + 13)/2 × h = 12.5h ≤ 12.5×5 = 62.5.

Adding the rectangle (area 2×5 = 10) gives total area ≤ 62.5 + 10 = 72.5. Of the choices given, only 70 is ≤ 72.5, so the composite area is 70 cm^2.