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Mr. Riojas is building his children a sandbox that is shaped like a triangular prism. He uses 7-foot-long wooden beams for each 'side of the base. He measures the height of the triangular base to be 6.1 feet. If he makes the sandbox 1 foot tall, how much sand will he need to fill it?

Respuesta :

isyllus

Answer:

21.35 [tex]ft^{3}[/tex]

Step-by-step explanation:

It is given that the box is a triangular prism.

Side of Base of prism = 7 ft

Height of Base of prism = 6.1 ft

Area of a triangle is given as:

[tex]B = \dfrac{1}{2} \times \text {Base} \times \text{Height}[/tex]

[tex]\Rightarrow \dfrac{1}{2} \times 7 \times 6.1\\\Rightarrow 21.35\ ft^{2}[/tex]

Volume of a prism is:

[tex]V = B \times h[/tex]

B is the area of base of prism

h is the height of prism

Here, h = 1 foot

So, V = 21.35 [tex]\times[/tex] 1

Volume of prism is = 21.35 [tex]ft^{3}[/tex]

Sand required to fill the triangular prism shape box is 21.35 [tex]ft^{3}[/tex].

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