In the square pyramid shown below, the slant height is 12 centimeters and the height of the pyramid is 7 centimeters.

To the nearest whole number, find the diagonal length of the base of the pyramid. In your final answer, include your calculations with reasoning for each step.

The lines which connect the two opposite corners of any quadrilateral are called diagonal. here we have a square pyramid whose slant height and the vertex height are given and we have to find the diagonal length of the base.

Let the side of the square base of the pyramid is "a". Now the side will be calculated by the following relation.

[tex](\dfrac{a}{2})^2[/tex] = s² - H

[tex](\dfrac{a}{2})^2[/tex] = 12² - 7 = 137

a² = 137 x 4 = 548

a = √548 = 23.40 cm

Now the diagonal will be calculated by using the Pythagorean theorem

D² = 23.04² + 23.40²

D² = 548 + 548

D = √1096

D = 33.10 centimeter

Therefore the diagonal of the square pyramid will be equal to 33.10 centimetres.

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In the square pyramid shown below, the slant height is 12 centimeters and the height of the pyramid is 7 centimeters. To the nearest whole number, find the diagonal length of the base of the pyramid. In your final answer, include your calculations with reasoning for each step.

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What is diagonal?

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In the square pyramid shown below, the slant height is 12 centimeters and the height of the pyramid is 7 centimeters.

To the nearest whole number, find the diagonal length of the base of the pyramid. In your final answer, include your calculations with reasoning for each step.