The sides of the base of a regular triangular pyramid are 10 cm, and the lateral edge is 13 cm.

| February 23, 2021 | education

The sides of the base of a regular triangular pyramid are 10 cm, and the lateral edge is 13 cm. The area of the side surface of the pyramid is?

The lateral surface of a regular triangular pyramid is three equal isosceles triangles. This means that the area of ​​the lateral surface will be equal to three areas of one face.

Sside = Sgr * 3.

The sides of the triangle (side face) are 13 cm, 13 cm and 10 cm.Calculate the area of ​​the triangle using Heron’s formula:

S = √ (p (p – a) (p – b) (p – c)), where p is the half perimeter of the triangle, a, b, and c are the sides of the triangle.

p = (13 + 13 + 10) / 2 = 36/2 = 18 (cm).

S = √ (18 * (18 – 13) (18 – 13) (18 – 10)) = √ (18 * 5 * 5 * 8) = √ (9 * 2 * 5 * 5 * 2 * 4) = √ (3² * 2² * 5² * 2²) = 3 * 2 * 5 * 2 = 60 cm².

Therefore, the lateral surface area is:

Side = 60 * 3 = 180 cm².



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