The area of the base of a regular quadrangular pyramid is 36 cm2. The lateral edge is 5 cm

The area of the base of a regular quadrangular pyramid is 36 cm2. The lateral edge is 5 cm. Find the apothem and the area of the lateral surface of the pyramid.

Given:

The area S of the base of a regular quadrangular pyramid is 36 cm2.

The side edge b of the pyramid is 5 centimeters.

Find the side of the base of the figure:

a = √S = √36 = 6 centimeters.

Apothema divides the side of the base into 2 parts, that is, 3 centimeters each.

Let’s find the value of the apothem h:

h = √ (b ^ 2 – a ^ 2) = √ (5 ^ 2 – 3 ^ 2) = √ (25 – 9) = √16 = 4 centimeters.

We calculate the area of the side surface of the pyramid by the formula S = 1/2 * a * h:

S = 1/2 * a * h = 1/2 * 6 * 4 = 12 cm2.

Answer: 4 centimeters, 12 cm2.