The area of a rectangle is given by the following equation:
[tex]A\text{ =}b\cdot h[/tex]
Where:
b = basis of the rectangle
h = height of the rectangle
Now, let's suppose that the basis is: b = 11
And from the statement we know that the diagonal is: d = 17
In order to find the area of the rectangle we need to find first the value of the height h. We can do that using Pitagoras theorem and the following picture:
Pitagoras theorem says that:
[tex]d^2=b^2+h^2[/tex]
The sum of the square of the cathetus is equal to the square of the hyphotenuse.
From the last equation we find the value of the height h:
[tex]\begin{gathered} h^2=d^2-b^2 \\ h=\sqrt[]{d^2-b^2}=\sqrt[]{17^2-11^2}=\sqrt[]{168}\cong12.96 \end{gathered}[/tex]
Using the last result we can compute the area of the rectangle:
[tex]A=b\cdot h\cong11\cdot12.96\cong142.58\cong142.6[/tex]
So the final answer is: 142.6 ft²
