# In a regular quadrangular pyramid, the apothem is 16, the lateral edge is 20. Find the height and side of the base.

August 22, 2021 | education

| Let’s denote the pyramid given by condition, SABCD, at the base – the square ABCD, SO – the height of the pyramid, point O – the center of the square, the point of intersection of the diagonals, SK – apothem. Consider a right-angled triangle SKA, find a leg AK – half of the side of the base.

AK = √ (SA² – SK²) = √ (400 – 256) = √144 = 12.

Base side:

AB = 2 * AK = 24.

Consider a right-angled triangle SOK and find a leg SO – the height of the pyramid.

SO = √ (SK² – OK²) = √ (256 – 144) = √112 = 4√7.

Answer: the side of the base is 24, the height of the pyramid is 4√7.

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