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” (see Figure ). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.

Answer 1

$\sf\fbox{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:Answer\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}$

$\bold\pink{Given:}$

$\sf{The \: sides \: of \: the \: wall \: are: \: 15 m, \: 11 m \: and \: 6 m.}$

$\bold\pink{To\:Find:}$

$\sf{The \:area \:painted\: in \:colour}$

$\bold\pink{Solution:}$

$\sf{The \: semi \: perimeter \: of \: triangular \: wall (s)}$

$\sf \: \implies \dfrac {(15+11+6)}{2 \: m} { \sf= 16 \: m}$

Using Heron’s formula,

$\sf{Area \: of \:the \: triangular \: wall}$

$\small\underline{\boxed{\sf\;\; \implies \sqrt{s(s - a)(s - b)(s - c) }}}$

$\sf\underline{\underline{Subsituting \: the \: values \: in \: the \: formula:}}$

$\sf{ = \sqrt { \bigg\lgroup 16(16-15)(16-11)(16-6)\bigg\rgroup}m^2}$

$\sf{=\sqrt{\bigg\lgroup16\times 1\times 5\times 10\bigg\rgroup} }$$\sf{m^2}$

${= \sf\sqrt{800} { m^2}}$

$\sf{= 20 \sqrt{2} {m}^{2}}$

Answer 2

We are given that the slide is a triangle and it's sides are 15 m, 11 m and 6 m.

We know,

Area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

and $s = \frac{1}{2}(a + b + c)$

∴ s = ½(15 + 11 + 6) m = 16 m

So, area = $\sqrt{16(16 - 15)(16 - 11)(16 - 6)}$

⇒ Area = $4 \sqrt{5 \times 10}$

⇒ Area = $4 \times 5 \sqrt{2}$

⇒ Area = $20 \sqrt{2}$ m² (ans.).

More:-

• The Heron's formula was discovered by an ancient mathematician from Greece.
• It was said that Pythagoras was a student of Thales.