Question

Find the area os the shaded region in Fig. 12.12.

Answer 1

Area of shaded region = 384 cm²

Explanation:

The question image is attached below.

Triangle ADB is a right triangle.

Using Pythagoras theorem,

$(\mathrm{AB})^{2}=(\mathrm{AD})^{2}+(\mathrm{BD})^{2}$

$A B^{2}=12^{2}+16^{2}$

$A B^{2}=144+256$

$A B^{2}=400$

Taking square root on both sides, we get

AB = 20 cm

In ΔADB, a = 20 cm, b = 12 cm, c = 16 cm

Using Heron's formula,

$A=\sqrt{s(s-a)(s-b)(s-c)}$,

where $S=\frac{a+b+c}{2}$

$S=\frac{20+12+16}{2}$

S = 24

$A=\sqrt{24(24-12)(24-16)(24-20)}$

$A=\sqrt{24 \times 12 \times 8 \times 4}$

A = 96 cm²

In ΔABC, a = 20 cm, b = 52 cm, c = 48 cm

$S=\frac{20+48+52}{2}$

S = 60

$A=\sqrt{60(60-20)(60-48)(60-52)}$

$A=\sqrt{60 \times 40 \times 12 \times 8}$

A = 480 cm²

Area of shaded region = Area of ΔABC – Area of ΔADB

                                      = 480 cm² – 96 cm²

                                      = 384 cm²

Area of shaded region = 384 cm²

To learn more...

1. Calculate the area of shaded region in the figure 11.3

https://brainly.in/question/1777121

2. Find the area of the shaded region in Fig. 17.12

https://brainly.in/question/9599761

Answer 2

Step-by-step explanation:

of shaded region = 384 cm²

Explanation:

The question image is attached below.

Triangle ADB is a right triangle.

Using Pythagoras theorem,

(\mathrm{AB})^{2}=(\mathrm{AD})^{2}+(\mathrm{BD})^{2}(AB)

2

=(AD)

2

+(BD)

2

A B^{2}=12^{2}+16^{2}AB

2

=12

2

+16

2

A B^{2}=144+256AB

2

=144+256

A B^{2}=400AB

2

=400

Taking square root on both sides, we get

AB = 20 cm

In ΔADB, a = 20 cm, b = 12 cm, c = 16 cm

Using Heron's formula,

A=\sqrt{s(s-a)(s-b)(s-c)}A=

s(s−a)(s−b)(s−c)

,

where S=\frac{a+b+c}{2}S=

2

a+b+c

$S=\frac{20+12+16}{2}

S = 24

A=\sqrt{24(24-12)(24-16)(24-20)}A=

24(24−12)(24−16)(24−20)

A=\sqrt{24 \times 12 \times 8 \times 4}A=

24×12×8×4

A = 96 cm²

In ΔABC, a = 20 cm, b = 52 cm, c = 48 cm

$S=\frac{20+48+52}{2}

S = 60

A=\sqrt{60(60-20)(60-48)(60-52)}A=

60(60−20)(60−48)(60−52)

A=\sqrt{60 \times 40 \times 12 \times 8}A=

60×40×12×8

A = 480 cm²

Area of shaded region = Area of ΔABC – Area of ΔADB

= 480 cm² – 96 cm²

= 384 cm²

Area of shaded region = 384 cm²