Question

which figure has a greater area? (left triangle: base 32 in, height 32 in (right triangle). right triangle: height 36 in, base 23 in (right triangle))

Explanation:

Step1: Calculate area of first triangle

The formula for the area of a triangle is \( A = \frac{1}{2} \times base \times height \). For the first triangle, base \( b_1 = 32 \) in and height \( h_1 = 32 \) in. So, \( A_1=\frac{1}{2}\times32\times32 \).
\( A_1 = 16\times32 = 512 \) square inches.

Step2: Calculate area of second triangle

For the second triangle, base \( b_2 = 23 \) in and height \( h_2 = 36 \) in. Using the area formula, \( A_2=\frac{1}{2}\times23\times36 \).
\( A_2 = 23\times18 = 414 \) square inches.

Step3: Compare the two areas

Since \( 512>414 \), the first triangle (with base 32 in and height 32 in) has a greater area.

Answer:

The triangle with base 32 inches and height 32 inches (the first triangle) has a greater area.