Question

which figure has a greater area?
two triangles with their bases and heights labeled: first triangle has height 72 yd and base 88 yd; second triangle has height 75 yd and base 95.7 yd

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 = 88 yd, height = 72 yd.
So, $A_1 = \frac{1}{2} \times 88 \times 72$.
First, $88 \times 72 = 6336$, then $\frac{1}{2} \times 6336 = 3168$ square yards.

Step2: Calculate Area of Second Triangle

For the second triangle, base = 95.2 yd, height = 75 yd. Using the same formula, $A_2 = \frac{1}{2} \times 95.2 \times 75$.
First, $95.2 \times 75 = 7140$, then $\frac{1}{2} \times 7140 = 3570$ square yards.

Step3: Compare the Areas

Compare $A_1 = 3168$ and $A_2 = 3570$. Since $3570 > 3168$, the second triangle (with base 95.2 yd and height 75 yd) has a greater area.

Answer:

The triangle with base 95.2 yd and height 75 yd (the second triangle) has a greater area.