Jan is 5 years older than Tom. In 3 years, Tom will be as old as Jan. What is Tom’s age now?

A composite figure is shown.

VikaD [51]

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

$S = 6l^{2}$

Where $l$ 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 = $5l^{2}$

From the given information,

$l = 6 \ feet$

∴ 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,

$S = 2l^{2} + 4lh$

Where $l$ is the length of the sides and

$h$ 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 = $2l^{2} + 4lh - 2l^{2}$

Surface area of the square prism in the figure = $4lh$

From the given information,

$l = 6 \ feet$

$h = 20 \ feet$

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

$S = l^{2} + 2l\sqrt{\frac{l^{2} }{4}+h ^{2} }$

Where $l$ is the base length

and $h$ 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 = $l^{2} + 2l\sqrt{\frac{l^{2} }{4}+h^{2} }\ - ( l^{2})$

Surface area of the pyramid part of the figure = $2l\sqrt{\frac{l^{2} }{4}+h^{2} }$

From the given information,

$l = 6 \ feet$

$h = 4 \ feet$

∴ Surface area of the pyramid part of the figure = $2(6)\sqrt{\frac{6^{2} }{4}+4^{2} }$

= $12\sqrt{\frac{36 }{4}+16}$

= $12\sqrt{9+16 }$

= $12\sqrt{25}$

= 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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4 0

2 years ago

If the area of a wall is 36 square meters, what is the perimeter?

JulsSmile [24]

Answer:

18

Step-by-step explanation:

it is 18 because you would 36 divided by 4 to get 9. Then you would do 9 plus 6 to get the answer 18

4 0

3 years ago

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One base of a triangular prism has two sides that are 15 inches wide and 10 inches long what is the possible length for the thir

Tcecarenko [31]

18.03 inches
Put the dimensions into the pythagorean theorem, that will give you the answer.

7 0

4 years ago

Evaluate –3² + (2 – 6)(10)<br> i got -72 some how oof

djverab [1.8K]

Answer: -49

Step-by-step explanation: hope this helps you and plz mark me as brainest

7 0

3 years ago

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Trains Two trains, Train A and Train B. weigh a total of 196 tons. Train A is heavier than Train B. The

aleksklad [387]

Answer:

Train A = 128

Train B = 68

Step-by-step explanation:

We can set up a system of equations for this problem

Let A = # of tons of Train A

Let B = # of tons of Train B

A + B = 196

A = B + 60

Now, we plug in A for the first equation, using substitution

(B+60) + B = 196

2B + 60 = 196

Subtract 60 from both sides

2B = 136

Divide both sides by 2

B = 68

Plug in 68 for B in the 2nd equation

A = 68 + 60

A = 128

Checking work: 128 + 68 = 196 :D hope this helped

5 0

2 years ago