Question

$\underline\mathcal\colorbox{yellow}{{\color{blue}{★Question  ★}}}$
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.

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Answer 1

Step-by-step explanation:

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Answer 2

$\underline\mathcal\colorbox{pink}{{\color{blue}{★Solution★}}}$

BE = AB - AE

= 12 cm - (AC + CE)

= 12 cm - (2.4 cm + 6 cm)

= 12 cm - 8.4 cm

= 3.6 cm

Area of △ACF = $\frac{1}{2} \times b \times h$ = $\frac{1}{2} \times CF \times AC$

ㅤㅤㅤㅤㅤㅤ =$\frac{1}{2} \times 3.6 \times 2.4 = 4.32 {cm}^{2}$

Area of the rectangle FCEG = l x b

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ= CE x CF

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ= 6 cm x 3.6 = $21.6 {m}^{2}$

Area of △GEB = $\frac{1}{2} \times b \times h$ = $\frac{1}{2} \times BE\times GE$

ㅤㅤㅤㅤㅤ= $\frac{1}{2} \times 3.6 \times 3.6 = 6.48 {cm}^{2}$

Area of △ABH = $\frac{1}{2} \times b \times h$ = $\frac{1}{2} \times AB\times DH$

ㅤㅤㅤㅤㅤ= $\frac{1}{2} \times 12 \times 2.4 = 14.4 {cm}^{2}$

ㅤ

Area of the polygon AFGBH = Area of △ACF + Area of rectangle FCEG + Area of △GEB + Area of △ABH

= 3.6 cm² + 4.32 cm² + 21.6 cm² + 6.48 cm² + 14.4 cm²

$\fbox \red{= 50.40 cm²}$

$\fbox \purple{Hence, the required area = 50.40 cm}$

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