Question

which figure has a greater area? 4 in 6 in 10 in 9 in 10 in

Explanation:

Step1: Calculate trapezoid area

The formula for the area of a trapezoid is $A=\frac{(a + b)h}{2}$, where $a = 4$ in, $b = 10$ in, and $h=6$ in. So $A_{trapezoid}=\frac{(4 + 10)\times6}{2}=\frac{14\times6}{2}=42$ square - inches.

Step2: Calculate triangle area

The formula for the area of a triangle is $A=\frac{1}{2}bh$, where $b = 10$ in and $h = 9$ in. So $A_{triangle}=\frac{1}{2}\times10\times9 = 45$ square - inches.

Step3: Compare areas

Since $42<45$, the triangle has a greater area.

Answer:

The triangle has a greater area.