Question

An umbrella is made by stitching 10 triangular pieces of cloth
of two different colours (shown in the adjoining figure), each
piece measuring 20 cm, 50 cm and 50 cm. How much cloth of
each colour is required for the umbrella?
Please help me to do this sum ​

Answer 1

$\huge\boxed{\fcolorbox{red}{blue}{Answer}}$

There are 10 triangles, out of which 5 of black and 5 of grey color. Now,

Area of of each cloth=5× area of 1 triangle

Area of triangle=

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

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

$\frac{50 + 20 + 50}{2} = 60$

Therefore, area of triangle =

$\sqrt{60(60 - 50)(60 - 20) (60 - 50)} = \sqrt{60 \times 10 \times 40 \times 10}$

$\sqrt{6 \times 10 \times 10 \times 4 \times 10 \times 10} = 2 \times 10 \times 10 \sqrt{6} = 200 \sqrt]{6cm ^{2} }$

Area of each cloth required=

$(5 \times 200\sqrt{6} )cm2$