Question

This is not multiple-choice, I need steps and how we found the answer, help I've been stuck for 2 days now!!!!

Find the surface area of the figure. Be sure to show all of your work and steps in solving for your answer.

Answer 1

Answer:The surface area of a figure is the sum of all the sides that consist of it.

Let's first find the base's area, using the formula for the area of a rectangle, L · W:

9(6)

= 54 is the area of the base.

Now let's find the entire front side of this figure's area and double it so we get both the areas of the front and back side (using the formula for the area of a rectangle):

4(9)[bottom front rectangle] + 4(5)[upper front rectangle]

36 + 20

= 56, now double that area to get the area of both the front and back side:

56(2)

= 112 is the area of both the entire front and back side of this figure.

Now let's figure out the area of the right whole side of this figure then double it so we get both the areas for the left and right sides.

But, if we look at the middle rectangle to the right and left sides, we can see that there is no value, so let's find the value first.

The total length across the figure is 9 inches.

And we are given that the rectangle above intersects with the total length, so let's exclude that from 9 inches.

9 - 4 = 5, so now the total length of the two rectangles beside the above rectangle is 5.

But we want to find the value of one side, so divide 5 by 2.

5/2 = 2.5 inches.

Now let's find the whole entire area of the right side to this figure.

5(6)[upper right rectangle] + 2.5(5)[flat middle right rectangle] + 6(4)[bottom right rectangle)

30 + 12.5 + 24

= 66.5, now double that area to get both the area of the right and left side.

66.5(2)

= 133, is the area of both the right and left side of this entire figure.

Finally, we add all those areas together to get the surface area:-

54 + 112 + 133

= 299 inches is the surface area for this figure.

Explanation:

Answer 2

The surface area of a figure is the sum of all the sides that consist of it.

Let's first find the base's area, using the formula for the area of a rectangle, L · W:

9(6)

= 54 is the area of the base.

Now let's find the entire front side of this figure's area and double it so we get both the areas of the front and back side (using the formula for the area of a rectangle):

4(9)[bottom front rectangle] + 4(5)[upper front rectangle]

36 + 20

= 56, now double that area to get the area of both the front and back side:

56(2)

= 112 is the area of both the entire front and back side of this figure.

Now let's figure out the area of the right whole side of this figure then double it so we get both the areas for the left and right sides.

But, if we look at the middle rectangle to the right and left sides, we can see that there is no value, so let's find the value first.

The total length across the figure is 9 inches.

And we are given that the rectangle above intersects with the total length, so let's exclude that from 9 inches.

9 - 4 = 5, so now the total length of the two rectangles beside the above rectangle is 5.

But we want to find the value of one side, so divide 5 by 2.

5/2 = 2.5 inches.

Now let's find the whole entire area of the right side to this figure.

5(6)[upper right rectangle] + 2.5(5)[flat middle right rectangle] + 6(4)[bottom right rectangle)

30 + 12.5 + 24

= 66.5, now double that area to get both the area of the right and left side.

66.5(2)

= 133, is the area of both the right and left side of this entire figure.

Finally, we add all those areas together to get the surface area:-

54 + 112 + 133

= 299 inches is the surface area for this figure.