Question

Q 41.- Q 45 are based on case study-I Case Study-I Students of class X make a design such that, the area of an equilateral triangle ABC is 17320.5 cm2 With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle. (Use p= 3.14 and 3 = 1.73205) A B C Answer the following questions 2 x B xh & 323 31222 2 33.3 000 22 3011 41. Find the length of side of DABC. (a) 200 cm (b) 105.5 cm (c) 210.3 cm (d) 200.5 cm (d) 100 cm 42. Find the radius circle. (a) 200 cm (b) 20 cm (c) 10 cm 43. Find the area of each sector, (a) 5233.3 cm? (b) 5223.3 cm? (c) 4233.3 cm? 44. Find the area of the shaded region (a) 17320.5 cm(b) 1620.5 cm? (c) 15700 cm? (d) 522.2 cm? 2 (d) 31400 cm 45. Find the perimeter of DABC. (a) 60 cm (b) 400 cm (c) 600 cm (d) 300 cm​

Answer 1

Answer:

Given AB=BC=AC

Area of Equilateral △ ABC = 17320.5cm

2

∴

4

3

×AB

2

=17320.5

∴ AB =200cm

Also, AB=2AD

∴ AD=100 cm =radius

Area of sector DAE + Area of sector DBF + Area of sector FCE

We know that area of sector =

360

θ

×π×r

2

=3×

360

60

×3.14×100×100

=15700cm

2

∴ Area of the shaded region = Area of equilateral triangle − Area of all sectors

=17320.5−15700

=1620.5cm

2