Question

An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see figure), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?

{See figure in attachment}​

Answer 1

$\bf\huge{CONSIDER}$

• The side of one triangular pieces of cloth of umberella is

$\bf\red{a=20 \: cm, \: b=50 \: cm , d=50 \: cm}$

$\bf\green{s = \frac{a + b + c}{2} } \\ \\ = \frac{20 + 50 + 50}{2} \\ \\ \: \bf\pink{ = \frac{120}{2} = 60 \: cm}$

$\bf{THEREFORE}$

• Area of one triangular pieces

$\bf\blue{ \sqrt{s(s - a)(s - b)(s - c)}} \\ \\ \bf \ \sqrt{60(60 - 20)(60 - 50)(60 - 50)} \\ \\\bf\pink{ \sqrt{60(40)(10)(10)}} \\ \\ \bf{200 \sqrt{6 \: {cm}^{2} } }$

$\bf\huge{NOW}$

• Area of 5 triangle of one colour

$\bf\orange{5(200 \sqrt{6} {cm}^{2} )} = \bf{1000 \sqrt{6} {cm}^{2} }$

$\bf{THEREFORE}$

• 1000 √6 cm² of cloth of each colour is required for the umbrella

Answer 2

Step-by-step explanation:

CONSIDER

The side of one triangular pieces of cloth of umberella is

\bf\red{a=20 \: cm, \: b=50 \: cm , d=50 \: cm}a=20cm,b=50cm,d=50cm

\begin{gathered}\bf\green{s = \frac{a + b + c}{2} } \\ \\ = \frac{20 + 50 + 50}{2} \\ \\ \: \bf\pink{ = \frac{120}{2} = 60 \: cm}\end{gathered}

s=

2

a+b+c

=

2

20+50+50

=

2

120

=60cm

\bf{THEREFORE}THEREFORE

Area of one triangular pieces

\begin{gathered}\bf\blue{ \sqrt{s(s - a)(s - b)(s - c)}} \\ \\ \bf \ \sqrt{60(60 - 20)(60 - 50)(60 - 50)} \\ \\\bf\pink{ \sqrt{60(40)(10)(10)}} \\ \\ \bf{200 \sqrt{6 \: {cm}^{2} } }\end{gathered}

s(s−a)(s−b)(s−c)

60(60−20)(60−50)(60−50)

60(40)(10)(10)

200

6cm

2

\bf\huge{NOW}NOW

Area of 5 triangle of one colour

\bf\orange{5(200 \sqrt{6} {cm}^{2} )} = \bf{1000 \sqrt{6} {cm}^{2} }5(200

6

cm

2

)=1000

6

cm

2

\bf{THEREFORE}THEREFORE

1000 √6 cm² of cloth of each colour is required for the umbrella