27. Find the area of the following polygon if AB = 12 cm, AC = 2.4 cm, CE = 6 cm, AD
4.8 cm, CF = GE = 3.6 cm, DH = 2.4 cm.
Answers
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Step-by-step explanation:
Given
A polygon
AB = 12 cm
AC = 2.4 cm
CE = 6 cm
AD = 4.8 cm
CF = GE = 3.6 cm
DH= 2.4 cm
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To Find
The Area
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Solution
We can observe that the above diagram consists of triangles and rectangles, so we will find their area separately and add them up.
Let's first find the area for the triangle GEB.
GE = 3.6 cm
BE = AB - AE
GB = x
Let's find BE.
BE = AB - AE
BE = 12 - (AC + CE)
BE = 12 - (2.4 + 6)
BE = 12 - 8.4
BE = 3.6 cm
∴ BE = 3.6 cm
Area of triangle = 1/2×base×height
=1/2×3.6×3.6
=1/2×12.96
=6.48
∴ The area of ΔGEB is 6.48 cm²
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Now let's find the area of rectangle GECF.
GE = CF = 3.6 cm
GF = CE = 6 cm
Area of rectangle = Length \times BreadthLength×Breadth
⇒ 3.6 × 6
⇒ 21.6
∴ The area of rectangle GECF is 21.6 cm²
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Now let's find the area of triangle CAF.
CF = 3.6 cm
FA = x
CA = AB - CB
CA = 12 - CB
CA = 12 - (CE + EB)
CA = 12 - (6 + 3.6)
CA = 12 - 9.6
CA = 2.4 cm
∴ CA = 2.4 cm
Area of triangle = 1/2×base×height
=1/2 × 2.4×3.6
= 1/2 ×8.64
= 4.32
∴ The area of ΔCAF is 4.32 cm²
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Let's find the area of triangle HDB
HD = 2.4 cm
BH = x
DB = AB - DA
DB = 12 - 4.8
DB = 7.2 cm
∴ DB = 7.2 cm
Area of triangle = 1/2× base × height
=1/2 × 7.2×2.4
=1/2×17.28
=8.64
∴ The area of ΔHDB is 8.64 cm²
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Let's find the area of triangle AHD
AH = x
AD = 4.8 cm
HD = 2.4 cm
Area of triangle = 1/2×b×h
=1/2 × 4.8 ×2.4
=5.76
∴ The area of ΔAHD is 5.76 cm²
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Now that we have got the area of all the figures in the diagram we will add the area of all of them to find the final answer.
6.48 cm² + 21.6 cm² + 4.32 cm² + 8.64 cm² + 5.76 cm² = 46.8 cm²
∴ The area of the given polygon is 46.8 cm²
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