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butalik [34]
2 years ago
5

Find the volume of the square based pyramid.

Mathematics
2 answers:
labwork [276]2 years ago
5 0
Finding the <span>height of the pyramid:

\left(\dfrac{6}{2} \right )^{\!\!2}+h^{2}=8^{2}\\ \\ \\ 3^{2}+h^{2}=8^{2}\\ \\ h^{2}=8^{2}-3^{2}\\ \\ h^{2}=64-9\\ \\ h^{2}=55\\ \\ h=\sqrt{55}\mathrm{~m}


Finding the base area:

S=6^{2}\\ \\ S=36\mathrm{~m^{2}}


Formula for the volume of the pyramid:

V=\dfrac{S\cdot h}{3}\\ \\ \\ V=\dfrac{36\cdot \sqrt{55}}{3}\\ \\ \\ V=\dfrac{\diagup\!\!\!\! 3\cdot 12\cdot \sqrt{55}}{\diagup\!\!\!\! 3}\\ \\ \\ \boxed{\begin{array}{c} V=12\sqrt{55}\mathrm{~m^{3}} \end{array}}

</span>
frozen [14]2 years ago
4 0
A = 1/3 * s^2 * h where s is a side of the base and h is the height.
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Two triangle are congruent when the shape and size of both the triangle are same. The given information is the SAS case.

To find the form of the case we need to know about the triangle congruence theorem.

<h3>What is triangle congruence theorem?</h3>

Two triangle are congruent when the shape and size of both the triangle are same.

Triangle congruence theorem are-

  • Angle-Side-Angle theorem (AAS)- This theorem states that two triangle is congruent when two angle and one side of the triangle are respectively equal to the two angles and same side of the other triangle.

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Given information-

Evelyn is 104 meters from the take off.

The angle of elevation of the plane is 12°.

The plane is 100 meters away from the takeoff point.

The distance is 100 meters and 104 meters. The other two sides , as are same and the angle of elevation is also same for this case (12 degrees).

Thus the two triangle formed which are congruent.

As above discussed the case of SAS exists for the triangle congruence theorem.

Hence the given information is the SAS case.

Learn more about the triangle congruence theorem here;

brainly.com/question/19258025

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Andy filled four glasses with water at different temperatures as shown under each glass.
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black

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Hmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
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