Q83. - Algebra 2

Question

The formula for the surface area S of a regular pyramid is $S=\frac{1}{2}Pl+B$, where P is the perimeter of the base, l is the slant height, and B is the area of the base. Find the surface area of the square based pyramid shown at the right.

Step-by-Step Solution

Answer

The required surface area is 105.

Step 1- Calculate the perimeter

Determine the addition of the sides of the base to calculate the perimeter.

$\begin{array}{c}P=5+5+5+5\\ =20\end{array}$

Step 2 – Calculate the area of the base

Determine the square of the side of the base to calculate its area.

$\begin{array}{c}B=5\times 5\\ =25\end{array}$

Step 3 – Perform the substitution

Substitute 20 in place of P, 25 in place of B and 8 in place of l into the provided formula.

$S=\frac{1}{2}\times 20\times 8+25$

Step 4 – Perform the simplification

Simplify the obtained equation.

$S=105$

Step 5- Make the conclusion

As nothing can be done further with the expression so obtained value of S is the required surface area.