What is (a) the lateral area and (b) the total surface area of a regular square pyramid with the length of each edge equal to 6? ( leave answers in simplest radical form )

• lateral area: 36√3 square units

• total surface area: (36 +36√3) square units

Step-by-step explanation:

The area of an equilateral triangle of side length s is given by ...

A = (√3)/4·s^2

Your pyramid has four (4) such faces of side length 6 units, so the total (lateral) area of the triangular faces is ...

LA = √3·(6 units)^2 = 36√3 square units

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Of course the area of the square base is simply the square of its edge length, so is ...

A = (6 units)^2 = 36 square units

That means the total surface area, the lateral area plus the base area, is ...

(36 +36√3) square units

20

step-by-step explanation: