Question

Heron's Formula class 9 NCRT Ex. 12.1 Q.3

Plz answer fast.​

Answer 1

${\bf \green{Q}\blue{u}\pink{e}\purple{s}\gray{t}\red{i}\orange{o}\green{n}}$

There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN” (see Attachment ). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour

${\bf \green{A}\blue{n}\pink{s}\purple{w}\gray{e}\red{r}}$

${\purple{\sf Given :-}}$

• 1st Side ⇒ 15 m
• 2nd Side ⇒ 11 m
• 3rd Side ⇒ 6 m

${\purple{\sf To \: Find :-}}$

• Area

${\purple{\sf Formula \: Used :- }}$

• $\tt s=\dfrac{a+b+c}{2}$

• $\tt \sqrt{s(s-a)(s-b)(s-c)}$

Note → s here refers to semi perimeter

$\implies\sf s=\dfrac{15+11+6}{2}$

$\implies\sf s=\dfrac{32}{2}$

$\implies\sf s=16$

Now,

$\sf \implies \sqrt{16(16-15)(16-11)(16-6)}$

$\implies \sf \sqrt{16 \times 1 \times 5 \times 10}$

$\implies \sf \sqrt{800}$

$\implies \sf 20\sqrt{2}$

${\green{ \underbrace{\boxed{\underline{\underline{\purple{ \tt \therefore 20\sqrt{2} \: m^{2} \: is \: the \: area }}}}}}}$

Answer 2

Question :-

There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN”. If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.

Answer with explanation :-

Given :-

• If the sides of the wall are 15 m, 11 m and 6 m

To Find :-

• The area painted in colour

Solution :-

Let,

• 1st side(a) = 15 m
• 2nd side(b) = 11 m
• 3rd side(c) = 6 m

We know that,

$\boxed{\sf s = \frac{a + b + c}{2}}$

Where,

• s = Semi-perimeter
• a = 1st side
• b = 2nd side
• c = 3rd side

Substitute the values we get,

$:\implies\sf s = \frac{15 + 11 + 6}{2}$

$:\implies\sf s = \frac{\cancel{32}}{\cancel2}$

$:\implies\sf s = 16$

We know that,

$\boxed{\sf\sqrt{s(s-a)(s-b)(s-c)}}\: \: (\bf Heron's\:formula)$

Where,

• s = Semi-perimeter
• a = 1st side
• b = 2nd side
• c = 3rd side

Substitute the values we get,

$=\sf\sqrt{16(16-15)(16-11)(16-6)}$

$= \sf\sqrt{16 \times 1 \times 5 \times 10}$

$= \sf\sqrt{800}$

$=\underline{\boxed{ \blue{\sf20\sqrt{2}\:m^{2}}}}$

$\green{\sf\therefore 20\sqrt{2}\:m^{2} \: the \: area \: painted \: in \: colour.}$