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Here are a few recommended readings before getting started with this lesson.
Tearrik began training at a newly opened gym in his neighborhood called Little Muscles. In the swimming area there are three pools. One is a circular pool with an area of $28.2$ square meters. Another is a rectangular pool with an area of $54$ square meters.
The shape of the third pool surprised Tearrik a little. It looks like the combination of half the circular pool with the rectangular pool.
What is the area of the third pool?
The wrestling room of the gym where Tearrik works out has a circular carpet with the gym's logo inside.
The area of the logo is the sum of the areas of the involved figures. Then, start by recalling the formulas for finding the area of the corresponding figures.
Figure  Area's Formula 

Rectangle  $A=ℓ⋅w$ 
Trapezoid  $A=2(b_{1}+b_{2})h $ 
Semicircle  $A=2πr_{2} $ 
Next, find the area of each of the pieces that make up the logo.
Figure  Dimensions (cm)  Area $(cm_{2})$ 

Green rectangle  $ℓ=40$ $w=20$ 
$A_{1}=40⋅20=800$ 
Purple trapezoid  $b_{1}=100$ $b_{2}=20$ $h=30$ 
$A_{2}=2(100+20)30 =1800$ 
Gray trapezoid  $b_{1}=180$ $b_{2}=100$ $h=30$ 
$A_{3}=2(180+100)30 =4200$ 
Gray rectangle  $ℓ=100$ $w=10$ 
$A_{4}=100⋅10=1000$ 
Red semicircle  $r=20$  $A_{5}=2π(20)_{2} ≈628.32$ 
Substitute values
Multiply
Add terms
$a⋅cb =ca⋅b $
Cross out common units
Cancel out common units
$a⋅1=a$
Calculate quotient
Round to $1$ decimal place(s)
Substitute values
Calculate power
Add terms
$LHS =RHS $
$a_{2} =a$
Calculate root
Rearrange equation
On the first floor of the gym, the weight room and the spinning room are connected by the locker room. The gym owner received many complaints about the current floor quality. The entire first floor, instead, will be covered using recycled yoga mats.
How many square meters of rubber matting does the gym owner have to buy?Add the areas of the two big rectangles and subtract the area of the locker room.
Notice that the three rooms together form a composite figure that is shaped as two overlapping rectangles.
The area of the entire floor is then the sum of the areas of the big rectangles minus the area of the locker room. The area of the locker room must be subtracted because it is common for both rectangles.
Room  Figure  Dimensions (ft)  Area $(ft_{2})$ 

Spinning  Upper Rectangle  $ℓ=50$ $w=45$ 
$A_{1}=50⋅45=2250 $

Weight  Lower Rectangle  $ℓ=55$ $w=40$ 
$A_{2}=55⋅40=2200 $

Locker  Small Rectangle  $ℓ=55−35=20$ $w=40−25=15$ 
$A_{3}=20⋅15=300 $

Substitute values
Add and subtract terms
The area of a regular polygon is half the perimeter times the apothem. The apothem is the distance from the center of the polygon to any of its sides. The handle is what is left when a small semicircle is removed from a large semicircle.
The area of a regular polygon is half the perimeter times the apothem.
The perimeter of a regular polygon is equal to the side length times the number of sides. In this case, the number of sides is $8$ and all of them have a length of $13.5$ centimeters.$p=108$, $a=16.3$
Multiply
$a⋅b1 =ba $
Calculate quotient
Semicircle  Radius (cm)  $A=21 πr_{2}$  Area $(cm_{2})$ 

Outer  $6.75$  $A_{1}=21 π(6.75)_{2}$  $A_{1}=71.57$ 
Inner  $6$  $A_{2}=21 π(6)_{2}$  $A_{2}=56.55$ 
$A_{1}=71.57$, $A_{2}=56.55$
Subtract term
Tearrik noticed a poster on the wall saying that the gym would soon open its second floor with a boxing room and a multipurpose room. The blueprint for the second floor is shown next.
Find the perimeter and area of the of the entire floor. Round the answer to the nearest integer. Every unit in the blueprint corresponds to $4$ meters.Use the coordinate plane to find the side lengths of the composite figure. The perimeter is the sum of the lengths of the exterior sides. Break down the figure into known figures and find the sum of their areas.
The first step involves finding the perimeter of the entire floor. After that, the area of the floor will be calculated.
Start by identifying the coordinates of the vertices of the blueprint and the lengths of the horizontal and vertical sides. Let $m$ be the length of the slant side of the entrance.
The value of $m$ can be calculated by substituting $(4,1)$ and $(0,4)$ into the Distance Formula.Substitute values
Notice that the entire floor can be broken down into some known figures.
The area of the floor is the sum of the areas of the involved figures.
Place  Figure  Dimensions  Area 

Entrance and locker room  Trapezoid  $b_{1}=6$ $b_{2}=3$ $h=4$ 
$A_{1}=2(6+3)4 =18$ 
Seating area, hall, and boxing room  Rectangle  $ℓ=8$ $w=6$ 
$A_{2}=8⋅6=48$ 
Multipurpose room without the stage  Rectangle  $ℓ=6$ $w=3$ 
$A_{3}=6⋅3=18$ 
Stage  Semicircle  $r=3$  $A_{4}=21 π(3)_{2}≈14.14$ 
Composite figures are everywhere, it is a matter of looking closely. For instance, a running track combines rectangles and semicircles.
Many traffic signs can also be decomposed into known figures. The traffic sign indicating the direction of a street is formed by a rectangle and a triangle. The traffic sign corresponding to no Uturn
combines two rectangles, a semicircle, and a triangle.