Area of a Triangle
Given a triangle of base length B and height length H, the area can be calculated by the formula:
[tex]A=\frac{B\cdot H}{2}[/tex]
The base and the height must be perpendicular.
The height of the given triangle is H=7 in. We need to calculate the length of the base.
We are providing a new image where a variable x is introduced to help us calculate the base length:
The triangle formed by the sides 9-7-x is right, so we can calculate the value of x by applying the Pythagora's Theorem:
[tex]7^2+x^2=9^2[/tex][tex]49+x^2=81[/tex]
Solving for x:
[tex]\begin{gathered} x^2=81-49=32 \\ x=\sqrt[]{32} \end{gathered}[/tex]
The length of the base is:
[tex]B=9+\sqrt[]{32}[/tex]
Thus, the area of the triangle is:
[tex]A=\frac{7\cdot(9+\sqrt[]{32})}{2}[/tex]
Calculating:
A = 51.3 square inches
