Question

Ans.q.no.16 (find the area of the shaded region)

Answer 1

Heya !!


Each sides of equilateral triangle = 10 cm



Area of an equilateral triangle = ✓3/4 × (Side)²


= ✓3/4 × (10)²



=> ✓3/4 × 100



=> 25✓3 cm² .


In right angled triangle CPB.


PB = 8 cm and BC = 10 cm



As we can see that triangle CPB is a right angled triangle . So we can apply Pythagoras theroem in triangle CPB.



By Pythagoras theroem ,

(CP)² = (CB)² - (PB)²



(CP)² = (10)² - (8)²

(CP)² = 100-64


(CP)² = 36


(CP) = ✓36 = 6 cm



Area of right angled triangle CPB = 1/2 × (PB) × (CP)



=> 1/2 × 8 × 6


=> 24 cm²


Required Area. = (Area of ∆ABC) - (Area of ∆CPB)




=> ( 25✓3) - (24) cm²




=> 25× 1.732 - 24 [ ✓3 = 1.732]



=> 43.3 - 24 cm²



=> 19.3 cm²



★ HOPE IT WILL HELP YOU ★