Question

Tri-Star Industries employs electrical, plumbing, and air conditioning technicians. Their home office is made up of three square buildings, one for each department, with a triangular atrium in the middle. If the area of the Plumbing building is 5,184 ft2 and the area of the A/C building is 900 ft2,

what is the area of the Electrical building?

Answer 1

6084
`\text{ft}^2`.

Explanation:

Please find the attachment.

We have been given that the home-office of Tri-star industries is made up of three square buildings, one for each department, with a triangular atrium in the middle. The area of the Plumbing building is 5,184
`\text{ft}^2` and the area of the A/C building is 900
`\text{ft}^2`.

We know that area of square is square of its side length. Since all building are squares, so to find the area of electrical building, we will use Pythagoras theorem.

`a^2+b^2=c^2`

We can see from our attachment that side length of electrical building is hypotenuse (c) of the right triangle.

Upon substituting our given information in Pythagoras theorem, we will get:

`5184+900=c^2`

`6084=c^2`

Therefore, the area of electrical building is 6084 square feet.