You can find the areas of polygons by breaking the polygons into smaller shapes. Then we can apply area formulas you already know.
Example 1 :
Find the area of the given polygon
Solution :
By drawing a horizontal line (FG) parallel to the side DC, we have divided the given polygon into two rectangles.
(i) ABFG is a rectangle
(ii) EGDC is also a rectangle
Area of ABFG :
Area of rectangle = Length x width
length (AF) = 8 ft and width AB = 5 ft
= 8 x 5 = 40 square feet ---(1)
Area of EGDC :
length (DC) = 7 ft and width DE = 3 ft
= 7 x 3 = 21 ft2 ---(2)
(1) + (2)
Area of given polygon
= Area of rectangle ABFG + Area of rectangle EGDC
= 40 + 21 = 61 ft2
Example 2 :
Find the area of the given polygon
Solution :
By drawing a horizontal line (DE) parallel to the side GF, we have divided the given polygon into two rectangles.
(i) ABCE is a rectangle
(ii) DEGF is also a rectangle
Area of rectangle ABCE :
Area of rectangle = Length x width
length (AC) = 20 yd and width AB = 15 yd
= 20 x 15 = 300 yd2 ---(1)
Area of DEGF :
length (DG) = 13 yd and width GF = 11 yd
= 13 x 11 = 143 yd2 ---(2)
(1) + (2)
Area of given polygon
= Area of rectangle ABCE + Area of rectangle DEGF
= 300 + 143 = 443 yd2
Example 3 :
Find the area of the given polygon
Solution :
By drawing a horizontal line, we have divided the given shape as two parts.
(1) BECF is a rectangle
(2) ABD is triangle
Area of the given polygon
= Area of rectangle BECF + Area of triangle ABD
Area of rectangle BECF :
length CF = 16 cm and width BC = 7 cm
= length x width
= 16 x 7
= 112 cm2 ----(1)
Area of triangle ABD :
Base BD = BE - DE => 16 - 8 => 8 cm
Height AB = AC - BC => 13 - 7 => 6
Area of triangle ABD = (1/2) x b x h
= (1/2) x 8 x 6 ==> 24 cm2----(2)
(1) + (2)
Area of the given polygon = 112 + 24 ==> 136 cm2
Example 4 :
Find the area of the given polygon
Solution :
By drawing a horizontal line, we have divided the given shape as two rectangles.
(1) ABCD is a rectangle
(2) CEFG is rectangle
Area of the given polygon
= Area of rectangle ABCD + Area of triangle DEFG
Area of rectangle ABCD :
length AB = 20 ft and
width AC = AG - CG => 60- 30 = 30 ft
= length x width
= 20 x 30
= 600 ft2 ----(1)
Area of triangle DEFG :
length GF = 60 ft and
width FE = 30 ft
= length x width
= 60 x 30
= 1800 ft2 ----(1)
(1) + (2)
Area of the given polygon = 600 + 1800 ==> 2400 ft2
Example 5 :
Find the area of the given polygon
Solution :
Extend the top edge and the right edge of the polygon.
By subtracting the area of triangle BFB from the rectangle ABCD. We can find the area of the given polygon.
Area of the given polygon
= Area of rectangle ABCD - Area of triangle GFB
Area of rectangle ABCD :
length AD = 36 inches and
width AB = 18 inches
= length x width
= 36 x 18
= 648 in2 ----(1)
Area of triangle GFB :
base FG = 9 inches and
Height FB = AB - AF ==> 36 - 18 ==> 18 inches
= (1/2) x base x height
= (1/2) x 9 x 18
= 81 in² ----(1)
Area of the given polygon = 648 - 81 = 567 in2
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Sep 03, 24 08:52 PM
Sep 02, 24 10:23 AM
Sep 02, 24 09:55 AM