Question

The perimeter of the base of a square pyramid is 96cm and its height is 16cm,
a. What is the length of a base edge?
b. What is the slant height?
c. Find the lateral surface.

Answer 1

Hint-The perimeter of the base of the pyramid is given to us and its height is also given. Use the basic formula for perimeter of square base, find base edge. Use the base edge to find slant height using Pythagoras theorem and hence the lateral surface area.

Complete step-by-step answer:
Perimeter of base of pyramid = 96cm
Height of pyramid = 16cm
Perimeter of square base = $4\times \left(side\right)$
$$\begin{gathered} 96=4\times side \\ or \\ side={\displaystyle \frac{96}{4}}=24cm \end{gathered}$$
Let slant height be $l$
$$\begin{gathered} l=\sqrt{{\left({\displaystyle \frac{side}{2}}\right)}^2+H^2} \\ =\sqrt{{\left({\displaystyle \frac{24}{2}}\right)}^2+{16}^2} \\ =\sqrt{{12}^2+{16}^2} \\ =\sqrt{144+256} \\ =\sqrt{400} \\ =20cm \end{gathered}$$
Lateral surface area
$$\begin{gathered} =2\times side\times l \\ =2\times 24\times 20 \\ =960c{m}^2 \end{gathered}$$
Note- Students must remember the formulas for surface areas and the volume of pyramids as well as different common figures. A pyramid is a structure whose outer surfaces are triangular and converge to a single step at the top, making the shape roughly a pyramid in the geometric sense.