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Chapter 12… exercise 12.3, 10th problem …

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Chapter 12… exercise 12.3, 10th problem Why can't we take the area of 3 quadrants and then subtract it from the area of the triangle? They have taken the area of 3 sectors

Posted by Samruddhi Br 4 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 4 years, 8 months ago

Solution:

ABC is an equilateral triangle.

∴ ∠ A = ∠ B = ∠ C = 60°

There are three sectors each making 60°.

Area of ΔABC = 17320.5 cm²

⇒ √3/4 ×(side)² = 17320.5

⇒ (side)² =17320.5×4/1.73205

⇒ (side)² = 4×10⁴

⇒ side = 200 cm

Radius of the circles = 200/2 cm = 100 cm

Area of the sector = (60°/360°)×π r²cm²

= 1/6×3.14×(100)²cm²

= 15700/3cm²

Area of 3 sectors = 3×15700/3 = 15700 cm²

Thus, area of the shaded region = Area of equilateral triangle ABC – Area of 3 sectors

= 17320.5-15700 cm²= 1620.5 cm²

0Thank You

ANSWER

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