Question

which figure has a greater area?
15.8 yd
12 yd
14.3 yd
13.7 yd
submit

Explanation:

Step1: Recall triangle area formula

The area of a right - triangle is given by \(A=\frac{1}{2}\times base\times height\).

Step2: Calculate area of blue triangle

For the blue (cyan) right - triangle, the base \(b = 12\) yd and the height \(h=15.8\) yd.
Using the formula \(A_1=\frac{1}{2}\times12\times15.8\).
First, calculate \(12\times15.8 = 189.6\). Then, \(\frac{1}{2}\times189.6=94.8\) square yards.

Step3: Calculate area of purple triangle

For the purple right - triangle, the base \(b = 13.7\) yd and the height \(h = 14.3\) yd.
Using the formula \(A_2=\frac{1}{2}\times13.7\times14.3\).
First, calculate \(13.7\times14.3=(14 - 0.3)\times(14+0.3)=14^{2}-0.3^{2}=196 - 0.09 = 195.91\). Then, \(\frac{1}{2}\times195.91 = 97.955\) square yards.

Step4: Compare the two areas

Since \(94.8<97.955\), i.e., \(A_1 < A_2\).

Answer:

The purple (pink) right - triangle has a greater area.