Question

An umbrella is made by stitching 10 triangular pieces of cloth of two different colours each piece measuring 30cm, 60cm, 60cm. How much cloth of each colour is required for Umbrella?

• A. \( 1015 \sqrt{45} \)
• B. \( 1125 \sqrt{15} \)
• C. \( 1220 \sqrt{45} \)
• D. \( 1235 \sqrt{15} \)

Answer 1

The Correct Option is B

Step 1: Semi-perimeter \(s=\frac{30+60+60}{2}=75\).
Step 2: Area \(=\sqrt{75\times45\times15\times15}=\sqrt{15^{5}}=225\sqrt{15}\) per triangle.
Step 3: Total for 10 triangles \(=2250\sqrt{15}\); per colour, half of that \(=1125\sqrt{15}\).
\[ \boxed{1125\sqrt{15}\text{ cm}^{2}} \]