Area of Composite Figures
Area of a composite figure
In this video you will learn how to find the area of three composite figures. Two of the composite figures are composed of rectangles and triangles. The other figure is composed of semi-circles.
Transcript
Welcome to MooMooMath where we upload a new Math video everyday. In this video we would like to work on finding the area of composite figures. A composite figure is a figure that is made up of more than one geometric shape. For instance, in this composite figure we have a rectangle and a triangle. In order to find the area find the area of the two shapes and then add them.
In this example we have a rectangle and we know the area of a rectangle is length times width.
We will multiply a length of 10 and a width of 6 which equals 60
Next we will have a triangle and the area formula of a triangle equals 1/2 base x height.
In this triangle we have a base of 6 because we know these two are equal. I will move the 6 over.
We have a height of 7 because you have a right triangle, and 6 x 7 = 42
1/2 x 42 = 21
Now we will combine those two areas.
The area of the rectangle 60 plus the area of the triangle 21 which gives you a total area of 81 and the unit measure is meters squared.
Lets work another.
In this composite figure we will the area of the shaded area.
We have a rectangle, and two smaller boxes.
In order to find the shaded area we will take area of the rectangle, and subtract out the two boxes.
This is tricky because we need to add 32 + 8 =40
The area of a rectangle is length times width
Length is 32 + 8 = 40
The width is 8 + 8 = 16
This will equal 40 x 16 = 640
Now we need to subtract these two boxes.
The area of these boxes will be length times width.
8 x8 =64
We have two of these so 64 x 2 = 128
The shaded area = 640 -128 = 512 feet squared
Since this is a measurement we make sure we include our unit of measure which is feet, and area is squared so it will be 512 feet squared.
In summary with this composite figure I found the total area and subtracted the area of the two boxes and came up with 512 feet squared.
Lets look at this last area of a composite figure problem
It looks tricky, but we just have two semi-circles.
Area of a semi-circle is 1/2 pi x radius squared.
The area of a circle is pi times radius squared.
A semi-circle is half of this.
Be careful, one semi-circle has a diameter of 6 and the other has a diameter of 5.
Remember the diameter of a circle is the diameter all the way across the circle, and the radius is half of this.
1/2 of 6 will be 3, and 1/2 of 5 = 2.5
Let's get the area of this first semi-circe
1/2 Pi times 3 squared.
Next I will take 1/2 pi 9 and 1/2 of 9 is 4.5, so the area of this semi-circle is 4.5pi
Remember when you work with pi is an exact answer, if you want an estimation you can multiply it by 3.14
Now we get the area of this semi-cirle
Take 1/2 pi X 2.5 squared
This is diameter and the radius is 1/2 the diameter.
1/2 times pi and 2.5 squared is 6.25
Next, 1/2 6.25 becomes 3.125 Pi
Now I will add these two areas.
4.5pi + 3.125pi = 7.625 pi
If you want an estimation 7.625 x 3.14 = 23.942 cm squared
Hope this helps, and MooMoMath uploads a new Math video everyday
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