Question

there is an umbrella with triangular 10 pieces and triangle pieces 60,60and 20 find the area of umbrellas​

Answer 1

Answer

Answer 2

QUESTION-:

there is an umbrella with triangular 10 pieces and triangle pieces 60 cm,60 cm and 20 cm  find the area of umbrellas

EXPLANATIO -:

In this question we will find the area of 1 piece(using herons formula) and then multiply the area by 10 .

So calculating area of 1 piece .

Using herons's formula-:

$\bf \red\bigstar \: \: \orange{ \underbrace{ \underline{ \bf\; Area=\sqrt{s(s-a)(s-b)(s-c)} }}}}$

Where s is semiperimetre=

$\longmapsto \boxed{\bf\;s=\frac{a+b+c}{2}}$

a,b,c are the sides of the triangle-:

Calculations-:

$\longmapsto \bf\; s=\frac{60+60+20}{2}\\\\\longmapsto \bf\;s=\frac{140}{2}\\\\\longmapsto \boxed{\bf\underbace\; s=70\;cm}$

Now putting values in the formula-:

$\dashrightarrow \bf\; Area=\sqrt{70(70-60)(70-60)(70-20)} \\\\\dashrightarrow \bf\; Area=\sqrt{70 \times10\times10\times50} \\\\\dashrightarrow \bf\; Area=\sqrt{2\times 5\times 7\times5\times2\times5\times2\times2\times5\times5} \\\\\dashrightarrow \bf\; Areaa=\sqrt{2^2\times2^2\times7\times5^2\times5^2\times5} \\\\\dashrightarrow Area=100\sqrt{35}$

So the area of 1 piece is 100√35 cm

Area of 10 pieces-:

→100√35×10

→1000√35

$\red\dashrightarrow\underline{\underline{\sf \green{Area \: of \: umbrella \:is\; 1000\sqrt{35} \: cm }} }$

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