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The surface area of the pyramid is 60 square feet
The surface area of the square prism is 480 square feet
The surface area of the cube is 180 square feet
The total surface area is 720 square feet
<h3>Area of Composite figures</h3>From the question, we are to calculate the surface area of each part of the composite figure
- For the cube
Surface area of a cube is given by
Where is the length of a side
But only have 5 surfaces of the cube are part of the composite figure
∴ Surface area of the cubic part of the figure =
From the given information,
∴ Surface area of the cubic part of the figure = 5 × 6²
Surface area of the cubic part of the figure= 180 square feet
- For the square prism
The surface area of a square prism is given by the formula,
Where is the length of the sides and
is the height
But the <u>square surfaces</u> are not part of the surface of the figure
∴ Surface area of the square prism in the figure =
Surface area of the square prism in the figure =
From the given information,
Thus,
Surface area of the square prism part of the figure = 4×6×20
Surface area of the square prism part of the figure = 480 square feet
- For the pyramid
The pyramid is a square pyramid
The surface area of a square pyramid is given by
Where is the base length
and is the height of the prism
But the <u>square base</u> is not part of the surface of the figure
∴ Surface area of the pyramid part of the figure =
Surface area of the pyramid part of the figure =
From the given information,
∴ Surface area of the pyramid part of the figure =
=
=
=
= 12 × 5
= 60 square feet
Hence, the surface area of the pyramid is 60 square feet
Thus,
The total surface area = 180 square feet + 480 square feet + 60 square feet
The total surface area = 720 square feet
Hence, the total surface area is 720 square feet
Learn more on Calculating area of composite figures here: brainly.com/question/13175744
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Answer:
- D. A translation 1 unit to the right followed by a 270-degree counterclockwise rotation about the origin
Step-by-step explanation:
<em>See the picture for better visual</em>
Take segments ST and S'T'. If we extend them they will intersect at right angle.
It is the indication that the rotation is 90° or 270° but not 180°, when the corresponding segments come parallel.
The QRST is in the quadrant IV and Q'R'S'T' is in the quadrant III, which mean the rotation is 90° clockwise or 270° counterclockwise.
<u>This rotation rule is:</u>
- (x, y) → (y, -x)
We also see the points S and T have x-coordinate of 5 but their images have y-coordinates of -6. It means the translation to the right by 1 unit was the step before rotation.
<u>We now can conclude the correct choice is D:</u>
- A translation 1 unit to the right followed by a 270-degree counterclockwise rotation about the origin
