Question

an umbrella is made by stitching 10 triangular peices of cloth of two different colours each measuring 20cm,50cm,50cm.how much cloth of each colour is required for the umbrella. please write this answer in notebook​

Answer 1

$\underline\red{\bold{Answer:-}}$$1000 \sqrt{6} \: \: {cm}^{2}$

Step-by-step explanation:

$\textsf{there are 10 triangles ,}$

$\textsf{5 triangles of blue colour}$

$\textsf{5 triangles of grey colour}$

$\textsf{area of each cloth = 5×(area of 1 triangle}$

$\Large\textsf{Area of triangle = }$

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

$\textsf{a= 50}$

$\textsf{b = 20}$

$\textsf{c= 50}$

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

$s = \LARGE \frac{50 + 20 + 50}{2}$

$s = \LARGE\frac{120}{2}$

$s = 60 \: cm$

$\textsf{Area of triangle =}$

$\sqrt{60(60 - 50)(60 - 20)(60 - 50)} {cm}^{2}$

$\sqrt{60 \times (10) \times (40) \times (10)} {cm}^{2}$

$\sqrt{6 \times ( {2}^{2} ) \times ( {10}^{4}) }$

$\sqrt{6 } \times \sqrt{2} \times {10 }^{2}$

$200 \sqrt{6} {cm}^{2}$

$\textsf{Thus,}$

$\textsf{Area of triangle =}$

$200 \sqrt{6} \: {cm}^{2}$

$\Large\textsf{area of each cloth required ,}$

$\textsf{ = 5× area of triangle }$

$(5 \times 200\sqrt{6} ) {cm}^{2}$

$1000 \sqrt{6} \: \: {cm}^{2}$

$\textsf{so , Area of each cloth required is}$$1000 \sqrt{6} \: \: {cm}^{2}$