Question

Find the surface area of the regular pyramid shown in the accompanying diagram. If necessary, express your answer in simplest radical form.

Answer 1

Answer:

The area of the pyramid is 360 unit²

Step-by-step explanation:

Given

Base Edge, a = 10

Height, h = 12

Required

Determine the surface area

The surface area of a regular pyramid is calculated as thus;

$A = a^2 + 2a\sqrt{\frac{a^2}{4} + h^2}$

Substitute values for a and h

$A = 10^2 + 2 * 10 * \sqrt{\frac{10^2}{4} + 12^2}$

Evaluate all squares

$A = 100 + 2 * 10 * \sqrt{\frac{100}{4} + 144}$

$A = 100 + 2 * 10 * \sqrt{25 + 144}$

$A = 100 + 2 * 10 * \sqrt{169}$

Take positive square root of 169

$A = 100 + 2 * 10 * 13$

$A = 100 + 260$

$A = 360$

Hence, the area of the pyramid is 360 unit²