Question

Find the areas of given polygons.
a &
D
4.5 cm
5 cm
12 cm
G
A
С
5.5 cm
В
Can someone give the full explanation to this.

Answer 1

$\: \: \underline{\bf{ \: Given:- \: }}$

• AD = 12cm
• EF = 4.5cm
• DC = 5cm
• BG = 5.5cm

$\: \: \underline{\bf{ \: Find:- \: }}$

• Area of the given polygon.

$\: \: \underline{\bf{ \: Solution:- \: }}$

we, know that

$\underline{\boxed{\sf Area \: of \: Triangle = \dfrac{1}{2} \times b \times h}}$

Using this Formula we can find the area of whole polygon.

So,

In ∆AED

$\dashrightarrow\sf Area \: of \: Triangle = \dfrac{1}{2} \times b \times h$

$\dashrightarrow\sf A_{1}= \dfrac{1}{2} \times AD \times EF$

where,

• AD = 12cm
• EF = 4.5cm

So,

$\dashrightarrow\sf A_{1}= \dfrac{1}{2} \times AD \times EF$

$\dashrightarrow\sf A_{1}= \dfrac{1}{2} \times 12 \times 4.5$

$\dashrightarrow\sf A_{1}= \dfrac{1}{2} \times 54$

$\dashrightarrow\sf A_{1}= \dfrac{54}{2}$

$\dashrightarrow\sf A_{1}=27 {cm}^{2}$

$\small{\therefore\sf A_{1}=27 {cm}^{2}}$

Now, In ∆ADC

$\dashrightarrow\sf Area \: of \: Triangle = \dfrac{1}{2} \times b \times h$

$\dashrightarrow\sf A_{2}= \dfrac{1}{2} \times AD \times DC$

where,

• AD = 12cm
• DC = 5cm

So,

$\dashrightarrow\sf A_{2}= \dfrac{1}{2} \times AD \times DC$

$\dashrightarrow\sf A_{2}= \dfrac{1}{2} \times 12 \times 5$

$\dashrightarrow\sf A_{2}= \dfrac{1}{2} \times 60$

$\dashrightarrow\sf A_{2}= \dfrac{60}{2}$

$\dashrightarrow\sf A_{2}=30 {cm}^{2}$

$\small{\therefore\sf A_{2}=30 {cm}^{2}}$

Now, In ∆ABC

$\dashrightarrow\sf Area \: of \: Triangle = \dfrac{1}{2} \times b \times h$

$\dashrightarrow\sf A_{3}= \dfrac{1}{2} \times BG \times AC$

where,

• BG = 5.5cm
• AC = 12cm

So,

$\dashrightarrow\sf A_{3}= \dfrac{1}{2} \times BG \times AC$

$\dashrightarrow\sf A_{3}= \dfrac{1}{2} \times 5.5\times 12$

$\dashrightarrow\sf A_{3}= \dfrac{1}{2} \times 66$

$\dashrightarrow\sf A_{3}= \dfrac{66}{2}$

$\dashrightarrow\sf A_{3}=33 {cm}^{2}$

Area of whole polygon

$\sf :\to A_{1} + A_{2} + A_{3}$

$\sf :\to 27 + 30 + 33 = 90 {cm}^{2}$

$\small{\underline{\sf \therefore Area \: of \: the \: given \: polygon \: 90 {cm}^{2}}}$

Answer 2

Step-by-step explanation:

12 cm long, its perimeter is. (a) 18 cm. (b) 27 cm. (c) 36 cm. (d) 54 cm. Fig. 9.7. Solution: ... Total area covered by both the paths ... Find the area of a parallelogram shaped shaded region.