# Find the area of the diagonal section of a regular quadrangular pyramid if the side of the base is 8 cm

March 31, 2021 | education

| **Find the area of the diagonal section of a regular quadrangular pyramid if the side of the base is 8 cm and the side edge is 10.**

The diagonal section of the pyramid will be a triangle, the sides of which will be the diagonal of the square at the base and two opposite side edges of the pyramid.

Find the diagonal d of the square:

d = √ (a ^ 2 + a ^ 2) = √8 ^ 2 + 8 ^ 2 = √128 = 8√2.

Find the semi-perimeter of the triangle p:

p = (10 + 10 + 8√2) / 2 = 10 + 4√2.

Using Heron’s formula, we find the cross-sectional area:

S = √ ((10 + 4√2) * (10 + 4√2 – 10) * (10 + 4√2-10) * (10 + 4√2-8√2)) = √ (4√2 * 4√2 * (10 + 4√2) * (10 – 4√2)) = 4√2 * √ (100 – 32) = 4√2 * √68 = 46.65 cm ^ 2.

Answer: 46.65 cm ^ 2.

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