Question

lea wants to build a toolshed in the backyard but is only using the area beyond the path running through the yard. how large would the shed be if it is triangular - shaped with sides of length 24 feet, 7 feet, and 25 feet? round to the nearest hundredth.

Explanation:

Step1: Check if it is a right - triangle

We use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 7\), \(b = 24\), \(c = 25\).
\(7^{2}+24^{2}=49 + 576=625\) and \(25^{2}=625\). So it is a right - triangle with legs \(a = 7\) and \(b = 24\).

Step2: Calculate the area of the triangle

The area formula for a right - triangle is \(A=\frac{1}{2}ab\).
Substitute \(a = 7\) and \(b = 24\) into the formula: \(A=\frac{1}{2}\times7\times24\).
First, calculate \(7\times24 = 168\). Then \(A=\frac{168}{2}=84.00\) square feet.

Answer:

84.00 square feet