# The base of the pyramid is a rectangle with sides 6 cm and 8 cm. All side edges are 13 cm. Find the volume of the pyramid.

July 23, 2021 | education

| 1. It is known that the volume of the pyramid V is equal to 1/3 of the product of the area S of the base by the height h.

2. According to the condition of the problem, it is given: at the base there is a rectangle with sides 6 cm and 8 cm, side edges L are 13 cm long.

The height h of the pyramid is lowered to the point of intersection of the diagonals d of the rectangle, its value is calculated by the Pythagorean theorem:

h² = L² – (1/2 d) ², whence h = √13² – 1/4 d².

D is determined from a right-angled triangle with legs 6 cm and 8 cm:

d = √6² + 8² = √36 + 64 = √100 = 10 cm.

So h = √169 – 1/4 * 100 = √144 = 12 cm.

3. Let’s calculate the V pyramid:

V = 1/3 * 6 cm * 8 cm * 12 cm = 192 cm³.

Answer: The volume is 192 cm³.

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