Combined figures :
Here we are going to see how to find the area and perimeter of combined geometric shapes. In our day to day life we see many combined shapes of triangle, rectangle,square and semi circle. To find the area and perimeter of such figures we need to calculate the area separately and then we can add them.
Find the perimeter and area of the following figures:
In the above figure we have four semi circles and one square. To find the perimeter of the above figure we have to add the sum of four semicircles and a square.
Diameter of each semicircle is 7 cm from this we can find the radius of semi circle.
Radius = 7/2 = 3.5 cm
Length of each side of square = 7 cm
The perimeter of the given figure = 4 (perimeter of semicircles) + Perimeter of square
Perimeter of semi circle AEB = Π r
= (22/7) x 3.5
= 22 x 0.5
Perimeter of 4 semi circles = 4 (11)
= 44 cm
Perimeter of square = 4a
here a = 7 cm
= 4 (7)
= 28 cm
The perimeter of the given figure = 44 cm + 28 cm
= 72 cm
Area of 1 semi circle = Π r²/2
= (1/2) x (22/7) x (7/2)²
= (1/2) x (22/7) x (7/2) x (7/2)
= (1/2) x 11 x (7/2)
= 19.25 cm²
Area of 4 semi circles = 4 (19.25)
Area of square = a²
= 7 x 7
= 49 cm²
Area of given figure = Area of 4 semi circles + Area of square
= 77 + 49
= 126 cm²
Find the area of shaded portion.
Area of shaded portion = Area of rectangle - Area of 4 quadrants of circle
Area of rectangle = L x W
Length of rectangle = 15 cm
Width of rectangle = 8 cm
= 15 x 8
= 120 cm²
Area of quadrant = Π r²/4
= [(22/7) x 3²]/4
= (22 x 3 x 3)/(7 x 4)
Area of 4 quadrant = 4 x 198/28
= 28.28 cm²
Area of shaded portion = 120 - 28.28
= 91.715 cm²
After having gone through the stuff given above, we hope that the students would have understood "Combined figures"
Apart from the stuff given above, if you want to know more about "Combined figures", please click here.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
MATH FOR KIDS
HCF and LCM word problems
Word problems on quadratic equations
Word problems on comparing rates
Converting repeating decimals in to fractions