Question

An umbrella is to be made by stitching 8 triangular pieces of cloth with lengths 17 cm, 17 cm and 16 cm. Find how much cloth is required for the umbrella.

Answer 1

Answer:

840 sq-cm of cloth is required .

Step-by-step explanation:

Area of triangle when all sides are given can be calculated by the Hero's Formula

$\boxed{Area \: of \: triangle = \sqrt{S(S - a)(S - b)(S - c)}}$

S= Semi-perimeter

a,b,c are sides of triangle

Area of given triangle a=17 cm

b= 17 cm

c= 16 cm

$S = \frac{a + b + c}{2} \\ \\S = \frac{17+17+16}{2} \\ \\S = 25$

Area of 1 triangular part:

${Area \: of \: triangle = \sqrt{25(25-17)(25-17)(25-16)}}$

$=\sqrt{25 \times 7 \times 7 \times 9} \\ \\ = 5 \times 3 \times 7 \\ \\ = 15 \times 7 \\ \\ =105 \: {cm}^{2}$

Total cloth required to make umbrella

$= 8 \times 105 \\ \\ = 840 \: {cm}^{2}$

Hope it helps you.