Question

which figure has a greater area? triangle with base 78 in, height 43 in; parallelogram with base 58 in, height 32 in submit

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 = 78 in and height = 43 in. So, $A_{triangle} = \frac{1}{2} \times 78 \times 43$. First, calculate $78 \times 43 = 3354$, then divide by 2: $\frac{3354}{2} = 1677$ square inches.

Step2: Calculate area of parallelogram

The formula for the area of a parallelogram is $A = base \times height$. Here, base = 58 in and height = 32 in. So, $A_{parallelogram} = 58 \times 32$. Calculating that: $58 \times 32 = 1856$ square inches.

Step3: Compare the two areas

Now, compare 1677 and 1856. Since $1856 > 1677$, the parallelogram has a greater area.

Answer:

The parallelogram (the second figure) has a greater area.