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goldfiish [28.3K]
3 years ago
13

Pls help!!!

Mathematics
1 answer:
FrozenT [24]3 years ago
6 0

Answer:

The height of the pyramid is 50\ in

Step-by-step explanation:

we know that

The volume of a triangular pyramid is equal to

V=\frac{1}{3}BH

where

B is the area of the base

H is the height of the pyramid

we have

V=1,800\ in^{3}

The area of the base B is equal to

B=\frac{1}{2}(12)(18)=108\ in^{2}

substitute and solve for H

1,800=\frac{1}{3}(108)H

5,400=(108)H

H=5,400/(108)=50\ in

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a. What is the name of the 3D shape?

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Step-by-step explanation:

a. What is the name of the 3D shape?

The 3D shape has two congruent and parallel faces (triangles) and the other faces are parallelograms, then the 3D shape is a prism


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c. What is the surface area of the figure?

The base of the prism is a triangle. Then to calculate the area of the base, we must use the formula to calculate the area of a triangle:

A_{b}=\frac{bh}{2}\\ A_{b}=\frac{(4 cm)(3 cm)}{2}\\ A_{b}=\frac{12cm^{2} }{2}\\ A_{b}=6cm^{2}

The perimeter of the base is the perimeter of the triangle, equal to the sum of the sides of the triangle:

P_{b}=4cm+3cm+5cm\\ P_{b}=12cm

h: Height of the prism is the distance between the bases of the prism (the triangle), then h=11 cm

Then, replacing in the formula the known values:

S=2(6 cm^{2})+(12 cm)(11 cm)\\ S=12 cm^{2}+132 cm^{2}\\ S=144 cm^{2}


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