What is the area of the trapezoid pictured to the right? (A) 22.5
(B) 24
(C) 27
(D) 45
(E) 54
Answer: A
Since the triangle is a right isosceles triangle, the other side of the triangle (the height of the trapezoid) must also be 3. The top base if the trapezoid must be 6 since it is the opposite side of a rectangle.
The area of a trapezoid = 1/2 (sum of parallel sides) × (distance between the parallel sides)
= 1/2 (9 + 6) (3) = 22.5
The area can also be found here by breaking up the figure into a rectangle (area of 6 × 3 = 18) and a triangle (area of ½ × 3 × 3 = 4.5) and adding these two areas.
The correct answer is A.
