In a regular rectangular truncated pyramid, the sides of the bases are 24 and 8 cm and the height is 15 cm

| February 11, 2021 | education

In a regular rectangular truncated pyramid, the sides of the bases are 24 and 8 cm and the height is 15 cm, find the total surface area.

It is known:

Regular quadrangular truncated pyramid;
The sides of the bases are 24 cm and 8 cm;
Height = 15 cm.
Find the total surface area.

1) Find the area of the base.

S main = 24 cm * 24 cm + 8 cm * 8 cm = 24 ^ 2 cm ^ 2 + 8 ^ 2 cm ^ 2 = 576 cm ^ 2 + 64 cm = 640 cm ^ 2.

2) Find the edge of the pyramid by the Pythagorean theorem.

l ^ 2 = h ^ 2 + ((24 – 8) / 2) ^ 2 = 15 ^ 2 + ((24 – 8) / 2) ^ 2 = 15 ^ 2 + (16/2) ^ 2 = 15 ^ 2 + 8 ^ 2 = 225 + 64 = 289 = 17 ^ 2;

Then: l = 17 cm;

3) Find the area of the lateral surface.

S side = 4 * l * (a + b) / 2 = 4 * 17 * (8 + 24) / 2 = 2 * 17 * (8 + 24) = 34 * 32 = 1088 cm ^ 2.

4) Find the total surface area.

S full = S side + S main = 1088 cm ^ 2 + 640 cm ^ 2 = 1728 cm ^ 2.



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