Question

which figure has a greater area? 8 ft 9 ft 5 ft 5 ft 9 ft

Explanation:

Step1: Calculate triangle area

The area formula for a triangle is $A_{triangle}=\frac{1}{2}\times base\times height$. Here, the base is $9$ ft and the height is $8$ ft. So $A_{triangle}=\frac{1}{2}\times9\times8 = 36$ square - feet.

Step2: Calculate trapezoid area

The area formula for a trapezoid is $A_{trapezoid}=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the parallel sides and $h$ is the height. Here, $a = 5$ ft, $b = 9$ ft and $h = 5$ ft. So $A_{trapezoid}=\frac{(5 + 9)\times5}{2}=\frac{14\times5}{2}=35$ square - feet.

Step3: Compare areas

Since $36>35$, the triangle has a greater area.

Answer:

The triangle has a greater area.