Question

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There is a diagram of the base of a bird feeder which is in the shape of a pentagonal prism. Each small square on the grid is 1 square inch.
The distance between the two bases is 8 inches. What will be the volume of the completed bird feeder?

The distance between the two bases is 8 inches. What will be the volume of the completed bird feeder?

Answer 1

Since this is the base, let us divide it into a rectangle and a triangle.

Triangle: 6 units wide 4 units tall

Formula: 1/2(base times height)

1/2(6 * 4) = 12 in ^2

Rectangle: 6 units long, 5 units tall

(6 * 5) = 30 in ^2

Add the two areas

30 + 12 = 42

Now to find volume, it is base times burger. Height is the 8 units

42 * 8 = 336

Volume = 336 in ^3

Answer 2

The area is the combination of the triangle and rectangle. Then the volume of the completed bird feeder is 336 cubic inches.

What is a pentagonal prism?

A pentagonal prism is a closed solid that has two parallel pentagon bases connected by a rectangle surface.

There is a diagram of the base of a bird feeder which is in the shape of a pentagonal prism.

Each small square on the grid is 1 square inch.

The distance between the two bases is 8 inches.

The volume of the completed bird feeder will be

Volume = Length × Area

The area is the combination of the triangle and rectangle.

Area = area of a triangle + area of a rectangle

Then the area of the triangle will be

$\rm Triangle \ area = \dfrac{1}{2} \times 6 \times 4\\\\Triangle \ area = 12 \ in^2$

Then the area of the rectangle will be

$\rm Rectangle \ area = 6 \times 5\\\\Rectangle \ area = 30 \ in^2$

Then the area will be

Area = 12 + 30

Area = 42 in²

Then the volume of the bird feeder will be

Volume = 8 × 42

Volume = 336 in³

More about the pentagonal prism link is given below.

https://brainly.com/question/21308574