the square base of the pyrmiad has an area of 144 square feet. if the slant height of the pyrimad is 10 feet what is the height of the pyrimad

The side length of the base is the square root of the area of the square, so is 12 ft. Then the distance from the center of one side to the center of the square base is 6 ft, The height of the pyramid completes a right triangle with side 6 ft and hypotenuse 10 ft. Then the height is given by the Pythagorean theorem as ...

height = √((10 ft)^2 - (6 ft)^2) = √(64 ft^2)

height = 8 ft

jainveenamrata jainveenamrata · Answer 2 · 2022-02-18T07:46:14+01:00

Using the Pythagoras theorem to solve the problem the height of the pyramid is 5.291 feet.

What is trigonometry?

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle. A right-angle triangle is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

Given

The square base of the pyramid has an area of 144 square feet.

If the slant height of the pyramid is 10 feet.

The diagonal of the square will be

[tex]\rm Diagonal = \sqrt{2* Area \ of\ square} \\\\\rm Diagonal = \sqrt{2*144} \\\\\rm Diagonal = 12* \sqrt{2}[/tex]

We know

[tex]\rm OC = \dfrac{AC}{2}\\OC = \dfrac{12\sqrt{2}}{2}\\OC = 6\sqrt2[/tex]

Then according to Pythagoras theorem.

[tex]\rm EC^2 = OC^2 + OE^2\\\\OE^2 = EC^2 - OC^2\\\\OE^2 = 10^2 - (6 \sqrt2)^2\\\\OE^2 = 100 - 36*2\\\\OE^2 = 100-72\\\\OE^2 = 28\\\\OE \ = 5.291[/tex]

Thus, the height of the pyramid is 5.291 feet.

More about the Trigonometry link is given below.

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