Question

which figure has a greater area?
trapezoid with top base 6.6 yd, height 10.3 yd, bottom base 18.3 yd
triangle with height 17.1 yd, base 9 yd
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Explanation:

Step1: Calculate area of trapezoid

The formula for the area of a trapezoid is $A = \frac{(a + b)}{2} \times h$, where $a = 6.6$ yd, $b = 18.3$ yd, $h = 10.3$ yd.
$A_{trapezoid}=\frac{(6.6 + 18.3)}{2} \times 10.3=\frac{24.9}{2} \times 10.3 = 12.45\times10.3 = 128.235$ square yards.

Step2: Calculate area of triangle

The formula for the area of a triangle is $A=\frac{1}{2} \times base\times height$, where base = 9 yd, height = 17.1 yd.
$A_{triangle}=\frac{1}{2} \times 9\times17.1 = 4.5\times17.1 = 76.95$ square yards.

Step3: Compare the two areas

Since $128.235>76.95$, the trapezoid (blue figure) has a greater area.

Answer:

The trapezoid (the blue figure with bases 6.6 yd, 18.3 yd and height 10.3 yd) has a greater area.