ACT Math · Area and volume

A trapezoid has parallel bases of length 8 and 14, and a height of 6. What is its area?

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A trapezoid has parallel bases of length 8 and 14, and a height of 6. What is its area?

Answer and explanation

Answer: J: 66

The area of a trapezoid is the average of the bases times the height: A=12(b1+b2)h=12(8+14)(6)=12(22)(6)=66A=\frac{1}{2}(b_1+b_2)h=\frac{1}{2}(8+14)(6)=\frac{1}{2}(22)(6)=66, choice J. You can check by thinking of the average width as 1111 and the height as 66, which gives 11⋅6=6611\cdot6=66. Choice G (132132) leaves out the factor of 12\frac{1}{2}, computing (8+14)(6)(8+14)(6). Choice H (8484) is 14⋅614\cdot6, treating the trapezoid as a rectangle with the longer base. Choice F (4444) is (8+14)⋅2(8+14)\cdot2, which does not relate to the height at all.

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