Question

The perimeter of a triangle is 30 cm and the circumference of its incircle is 88 cm. The area of the triangle is
(a)70 cm²
(b)140 cm²
(c)210 cm²
(d)420 cm²

Answer 1

Answer:

The area of ∆ABC is 210 cm².

Among the given options option (c) 210 cm² is the correct answer.

Step-by-step explanation:

Given :  

Perimeter of a triangle = 30 cm

AB + BC + CA = 30 cm ………..(1)

Circumference of the incircle = 88

Circumference of the incircle = 2πr

88  = 2πr

88 = 2 × 22/7 × r

88 = 44r/7

r = (88 × 7)/44

r = 2 × 7  

r = 14 cm

Radius of incircle , r = 14 cm

OR = OP = OQ = r  

Area of ∆AOB + Area of ∆BOC + Area of ∆AOC = Area of ∆ABC

(½ × AB × OR) + (½ × BC × OP) + (½ × AC × OQ) = Area of ∆ABC

Area of ∆ABC = (½ × AB ×r) + (½ × BC × r) + (½ × AC ×r)

= ½ r [AB + BC + CA]

= ½ × 14 [30]  

[From eq1 ]

= 7 × 30

= 210 cm²

Area of ∆ABC = 210 cm²

Hence, the area of ∆ABC is 210 cm².

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

The perimeter of a triangle is 30 cm and the circumference of its incircle is 88 cm. The area of the triangle is
(a)70 cm²
(b)140 cm²
(c)210 cm²
(d)420 cm², ✔✔


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The perimeter of a triangle is 30 cm and the circumference of its incircle is 88 cm. The area of the triangle is 420 cm².