Question

QueSUUl relp Heloise is drawing the design of the awning shown. The 2 triangular sections are identical isosceles triangles. Complete parts a and b. 3 ft 6 ft a. Write numbers in the boxes to show the missing dimensions. The number in the bottom left box is ft. The number in the middle box is ft. The number in the bottom right box is ft. (Type whole numbers or decimals.)

Answer 1

a. The number in the bottom left box is 6 ft. The number in the middle box is 3 ft. The number in the bottom right box is 6 ft.

b. The total area of the awning is 54 ft²

Step-by-step explanation:

An isosceles triangle is a triangle that has 2 equal sides.

So, the height and base of the triangles will be the same. It means that the number in the bottom left box is 6 ft and the number in the bottom right box is also 6 ft.

On the other hand, the number in the middlebox is the width of the rectangle, so it is 3 ft.

Then, the answers are:

The number in the bottom left box is 6 ft. The number in the middle box is 3 ft. The number in the bottom right box is 6 ft.

Now, the area of the awning can be calculated as the sum of the area of the isosceles triangles and the area of the rectangle.

The area of the triangles can be calculated as:

`\text{Area Triangle = }\frac{Base\text{ }*\text{ Height}}{2}`

Where the base and the height are equal to 6 ft, so the area is:

`\text{Area triangle = }\frac{6\text{ ft }*\text{ 6 ft}}{2}=(36ft^2)/(2)=18ft^2`

In the same way, the area of the rectangle is equal to:

Area Rectangle = Base x Height

Area Rectangle = 3 ft x 6 ft

Area Rectangle = 18 ft²

Finally, the total area of the awning is equal to:

Area = Area Rectangle + 2(Area Triangle)

Area = 18 ft² + 2(18 ft²)

Area = 18 ft² + 36 ft²

Area = 54 ft²

So, the total area of the awning is 54 ft²