Question

7 in. 6in. 9 in. it's the formula of a triangle

Answer 1

Area of a Triangle

Given a triangle of base length B and height length H, the area can be calculated by the formula:

`A=(B\cdot H)/(2)`

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:

`7^2+x^2=9^2`
`49+x^2=81`

Solving for x:

`\begin{gathered} x^2=81-49=32 \\ x=\sqrt[]{32} \end{gathered}`

The length of the base is:

`B=9+\sqrt[]{32}`

Thus, the area of the triangle is:

`A=\frac{7\cdot(9+\sqrt[]{32})}{2}`

Calculating:

A = 51.3 square inches