Question

An umbrella is made by stitching 12 triangular pieces of clothes , each measuring (50cm×20cm×50cm . find the area of the cloth used in it .​

Answer 1

Given :

• An Umbrella is made by stitching 12 triagular pieces each measuring 50cm , 20cm , 50cm

To Find :

• Area of cloth used in it.

Solution :

• a = 50cm
• b = 20cm
• c = 50cm

$\longmapsto\tt{s=\dfrac{a+b+c}{2}}$

$\longmapsto\tt{s=\dfrac{50+20+50}{2}}$

$\longmapsto\tt{s=\cancel\dfrac{120}{2}}$

$\longmapsto\tt\bold{s=60cm.}$

Now ,

$\longmapsto\tt{Area=\sqrt{s(s-a)(s-b)(s-c)}}$

$\longmapsto\tt{\sqrt{60(60-50)(60-20)(60-50)}}$

$\longmapsto\tt{\sqrt{60\times{10}\times{40}\times{10}}}$

$\longmapsto\tt{\sqrt{10\times{6}\times{10}\times{10}\times{2}\times{2}\times{10}}}$

$\longmapsto\tt{10\times{10}\times{2}\sqrt{6}}$

$\longmapsto\tt\bold{200\sqrt{6}{cm}^{2}}$

So , The Area of Triangle is 200√6cm².

Now ,

$\longmapsto\tt{5\times{200\sqrt{6}}}$

$\longmapsto\tt\bold{1000\sqrt{6}{cm}^{2}}$

So , The Total Cloth used in it is 1000√6cm²..