Question

The picture below shows the shape of a design painted on the side of a building. The design was formed by combining triangles and rectangles.

What is the area of the wall covered by the design?

A) 321 ft^2

B) 261 ft^2

C) 434 ft^2

D) 296 ft^2

Answer 1

Answer: 261^2

Explanation:

We have a rectangle, a square and a triangle.

We already know the area of the square is 6²=36ft²

The rectangle would be (16-6)×19=190ft²

Now finding the area of the triangle is quite tricky as we don't have a height, but we do know its sides

We know that one leg has to be 10, and the other is 26-19=7. Using the pythagorean theorem we get the hypothenuse=12.21

Now we can use Heron's Formula.

Using s=a+b+c/2 we get s=14.605

Answer 2

261 ft²

Explanation:

We have a rectangle, a square and a triangle.

We already know the area of the square is 6²=36ft²

The rectangle would be (16-6)×19=190ft²

Now finding the area of the triangle is quite tricky as we don't have a height, but we do know its sides

We know that one leg has to be 10, and the other is 26-19=7. Using the pythagorean theorem we get the hypothenuse=12.21

Now we can use Heron's Formula.

Using s=a+b+c/2 we get s=14.605

Now we can use the formula:

`area = √(s(s - a)(s - b)(s - c))`

Using this formula we get that the area of the triangle=35.

Add all three areas together: 35+36+190=261ft²