Question

Calculate the area of shaded region.
Chapter 12. Heron’s formula

Answer 1

in triangle, ABO,

Area = 1/2 * base * height

= 1/2 * 12 * 5

=30 cm²

By Pythagoras theorem,

AB = √AO²+BO²

AB= 13 cm

in triangle ABC, Area= √s(s-a)(s-b)(s-c)

s= perimeter/2

= 42/2

= 21 cm

area= √21(21-15)(21-14)(21-13)

= 2*3*2*7

= 84cm²

Area of shaded region= Area of triangle ABC- Area of triangle ABO

= 84- 30

= 54cm². (ANSWER)

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Answer 2

Step-by-step explanation:

AO=12cm

BO=5cm

We will find the AB by Pythagoras theorem

Pythagoras theorem=> B square + P square=H square

H=√(5×5)+(12×12)

H=√25+144

H=√169

H=13

Area of right angle triangle =1/2 × b ×h

=1/2×5×12

=30 sq. cm

Area of triangle =

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

√21(21-14)(21-15)(21-13)

√21×7×6×8

84 sq. cm

Area of shaded region = Area of larger triangle - Area of smaller triangle

84-30=54 sq. cm