## Find the volume of a regular triangular pyramid if it has height h=12 cm, base edge b=10 cm and height of the triangular base hb ≈ 8.7 cm.

Question

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## Answers ( )

Answer:116 cubic cmStep-by-step explanation:Volume of any pyramid is given by = 1/3(area of base* height of the pyramid)

To find the volume of given pyramid given are step

step 1:

Base of pyramid is triangular

base edge = 10 cm

height of triangular base = 8.7 ( This base is height of triangle and should not be confused with height of pyramid)

formula for area of triangle = 1/3(base * height)

substituting the value given above into the formula for area of triangle we have

area of base of pyramid = 1/3(10 * 8.7) = 29____________________________________________________

step two : find the volume of prism

height of prism = 12 cm

Volume of any pyramid= 1/3(area of base* height of the pyramid)

=> Volume of the given pyramid= 1/3(29* 12) = 116 cubic cmAnswer:The Answer is actually 174cm³ — I checked

Step-by-step explanation:1. Since the formula for the volume of a pyramid is Volume = (Area of the Base*The height of the pyramid)/3, you have to find the area of the base first. Since it is a triangular pyramid, it’s base is a triangle, and the area of a triangle is (base*height)/2, you plug in the Base Edge, which is 10 times the Height of the Base which is 8.7. 10*8.7 is 87 and 87/2 is 43.5.

2. Then, since you know the Area of the Base and the Height, you plug them into the equation. 43.5*12=522, and 522/3=174.

3. That means that 174cm³ is your answer.

— Hope this Helped —