Question

Each length with this mark is (I) is 36 inches(II) is 18 inches(III) is 30 inchesEach end has a height (from the highest point to the lowest point) of 28 inches.Part A If Wendell were to slice the doghouse in half with a slice parallel to the pentagonal bases, what shape would the slice be? Answer: Part B If Wendell were to slice the doghouse with a plane parallel to the two sides through any section of the doghouse, what shape would the slice be? Answer: Part C If Wendell were to slice the doghouse with a plane parallel to the bottom through any section of the doghouse, what shape would the slice be? Answer: Part DWendell plans to paint the doghouse after it's built. He wants to know what the surface area of the outside of the doghouse will be. To find the surface area, rst break up any composite shapes into rectangles and triangles. Which shape is considered a composite shape? When the shape is decomposed, what are the dimensions of the resulting shapes necessary for finding surface area?Answer: Part E Using the results from part D and the dimensions of the other surfaces, find the surface area of the outside of the doghouse. Be sure to include the bottom surface in your calculation. Answer: Part F.Wendell is curious how much space Jordan will have inside the doghouse to move around in. What is the volume of the doghouse? Answer:

Answer 1

Part A

If Wendell were to slice the doghouse in half with a slice parallel to the pentagonal bases, what shape would the slice be?

pentagonal shape is the answer part A

Part B

If Wendell were to slice the doghouse with a plane parallel to the two sides through any section of the doghouse, what shape would the slice be?

Answer: Rectangle

Part C If Wendell were to slice the doghouse with a plane parallel to the bottom through any section of the doghouse, what shape would the slice be?

Answer: Rectangle

Part D

Wendell plans to paint the doghouse after it's built. He wants to know what the surface area of the outside of the doghouse will be. To find the surface area, rst break up any composite shapes into rectangles and triangles. Which shape is considered a composite shape? When the shape is decomposed, what are the dimensions of the resulting shapes necessary for finding surface area?

The end is cnsidered a composite shape (rectangle + triangle)

When the shape is decomposed,

the dimensions are

A rectangle of 18 in x 30 in

and

A triangle with base 30 in and height 10 in (28-18)

Part E

Using the results from part D and the dimensions of the other surfaces, find the surface area of the outside of the doghouse. Be sure to include the bottom surface in your calculation.

Remember that the surface area is the area of its seven faces

so

SA=4(18)(36)+1(30(36)+2[(18)(30)+(1/2)(30)(10)]

SA=2,592+1,080+1,080+300

SA=5,052 in2

Part F.

Wendell is curious how much space Jordan will have inside the doghouse to move around in. What is the volume of the doghouse?

Answer:​

The volume of the composite figure is equal to the area of the pentagonal face multiplied by the distance between the two pentagonal bases

so

area of pentagonal face=[(18)(30)+(1/2)(30)(10)]=1,380 in2

the distance is equal to=36 in

V=1,380(36)

V=49,680 in3