An umbrella is made by stitching 12 triangular pieces of cloth, each measuring

We know that the triangle is an isosceles triangle.
Thus, we can find out the area of one triangular piece of cloth.

Area of isosceles triangle $=\frac{b}{4} \sqrt{4 a^{2}-b^{2}}$

$=\frac{20}{4} \times \sqrt{4(50)^{2}-20^{2}} \quad(a=50 \mathrm{~cm}$ and $b=20 \mathrm{~cm})$

$=5 \times \sqrt{10000-400}$

$=5 \times \sqrt{9600}$

$=5 \times 40 \sqrt{6}$

$=200 \sqrt{6}$

$=490 \mathrm{~cm}^{2}$

Now,
Area of 1 triangular piece of cloth = 490 cm2

Area of 12 triangular pieces of cloth $=12 \times 490=5880 \mathrm{~cm}^{2}$