Question

which figure has a greater area?
19 in
18 in
8.1 in
12 in
16.9 in
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Explanation:

Step1: Calculate area of triangle

The formula for the area of a triangle is $A = \frac{1}{2} \times base \times height$. Here, base = 18 in, height = 19 in. So, $A_{triangle} = \frac{1}{2} \times 18 \times 19 = 9 \times 19 = 171$ square inches.

Step2: Calculate area of trapezoid

The formula for the area of a trapezoid is $A = \frac{1}{2} \times (a + b) \times h$, where $a = 8.1$ in, $b = 16.9$ in, $h = 12$ in. So, $A_{trapezoid} = \frac{1}{2} \times (8.1 + 16.9) \times 12 = \frac{1}{2} \times 25 \times 12 = 12.5 \times 12 = 150$ square inches.

Step3: Compare the areas

Since $171 > 150$, the triangle has a greater area.

Answer:

The triangle (the first figure) has a greater area.