Question

Find the parimerlter and area of the room. please show work. ​

Answer 1

Answer: Perimeter = 38 ft, Area = 78 ft²

Explanation:

Perimeter:

Start at the top left corner and "walk" around the outside of the object until you get back to the starting point of your "walk":

P = 8 + 5 + 4 + 11 + 5 + 5

= 38

Area:

Separate the composite figure into two shapes (rectangle & triangle). Find the area of each shape and then add them together.

`A_(\ rectangle)=length* width\\.\qquad \qquad=8(5+4)\\.\qquad \qquad=8(9)\\.\qquad \qquad=72\\\\\\A_(\ triangle)=(1)/(2)* base* height\\\\.\qquad \qquad=(1)/(2)* (11-8)* 4\\\\.\qquad \qquad=(1)/(2)* 3* 4\\\\.\qquad \qquad=(1)/(2)* 12\\\\.\qquad \qquad=6\\\\\\A_(\ composite)=A_(\ rectangle)+A_(\ triangle)\\.\qquad \qquad=72+6\\.\qquad \qquad=78\\`

Answer 2

Perimeter = 38 feet

Area = 78 sq. feet

*Don't forget the squared (sq.) part in the area or your units WILL be wrong*

Explanation:

• Perimeter

We are just going to add up the sides given.

8 + 5 + 5 is the top rectangle

4 + 11 is the bottom rectangle and the bottom of the triangle

Add 5 more to account for the hypotenuse of the triangle.

8 + 5 + 5 + 4 + 11 + 5 or 8 + 5(3) + 4 + 11 = 38.

Your perimeter is 38 feet

• Area

The area of the top rectangle can be found by doing the length (8 ft.) times the width (5 ft.) 8 x 5 = 40 sq. ft.

The bottom rectangle has the same length as the top since they share a side but, has its own width (4 ft.). 4 x 8 = 32 sq. ft.

Time to add on the area of the triangle. The height of the triangle is the width of the bottom rectangle which is 4 ft. Now we use that 11 feet. The base of the triangle plus the length of the bottom rectangle equals 11 feet. We found from the previous parts that the length of the rectangles are 8. So if we subtract 8 from 11, we get the size of the base. 11 - 8 = 3. The base of the triangle is 3 feet.

Area of a right triangle is found by doing 1/2 times the base times the height. So the area of that triangle is (1/2)(3)(4) = (1/2)(12) = 6 sq. ft.

Now, we add all of our areas together.

40 + 32 + 6 = 78 sq. ft.