Question

Study Surface Area and Volume of Pyramid and Cone. How to find lateral area and total surface area of pyramid? please include one(1) problem per question with solutions.

Answer 1

Let's apply the formula for the lateral area and total surface area of a pyramid.

• Lateral Surface Area:

To find the lateral area of a pyramid, apply the formula:

$A_l=\frac{1}{2}ps$

Where:

p is the perimeter of the base

s is the slant height.

Example:

From the above square base pyramid, we have:

length of base, b = 4 cm

Slant height, s = 3 cm

Let's find the lateral area.

Since the base is a square, the perimeter will be:

p = 4 x 4 = 16 cm

Hence, to find the lateral area, we have:

$\begin{gathered} A_l=\frac{1}{2}ps \\ \\ A_l=\frac{1}{2}\times16\times3 \\ \\ A_l=24\operatorname{cm}^2 \end{gathered}$

Therefore, the lateral area of the square base pyramid above is 24 cm².

• Total surface area of a pyramid.

To find the total surface area of a pyramid, apply the formula:

$A_s=\frac{1}{2}Ps+A$

Where:

A is the area of the base

p is the perimeter of the base

s is the slant height.

Or we can simply say, the formula for total surface area is:

Total surface area = Lateral area + Area of base

Example:

Using the squarea base pyramid above, we have:

Area of base = 4 x 4 = 16 cm²

Lateral area = 24 cm²

Total surface area = 24 cm² + 16 cm² = 40 cm².