Question

1. find the area of this shape. dimensions are in feet.

Explanation:

Step1: Calculate the area of the right - triangle

The formula for the area of a right - triangle is \(A_{\triangle}=\frac{1}{2}\times base\times height\). Here, the base \(b = 10\) feet and the height \(h=24\) feet.

$$A_{\triangle}=\frac{1}{2}\times10\times24 = 120$$

Step2: Calculate the area of the semicircle

First, find the radius of the semicircle. The hypotenuse of the right - triangle is the diameter of the semicircle. Using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\) (where \(a = 10\), \(b = 24\)), \(c=\sqrt{10^{2}+24^{2}}=\sqrt{100 + 576}=\sqrt{676}=26\) feet. So the radius \(r=\frac{26}{2}=13\) feet.
The formula for the area of a semicircle is \(A_{semicircle}=\frac{1}{2}\pi r^{2}\). Substituting \(r = 13\) and \(\pi\approx3.14\), we get \(A_{semicircle}=\frac{1}{2}\times3.14\times13^{2}=\frac{1}{2}\times3.14\times169 = 265.33\)

Step3: Calculate the total area

The total area \(A=A_{\triangle}+A_{semicircle}\)

$$A=120 + 265.33=385.33$$

Answer:

\(385.33\) square feet