# NCERT Solutions For Class 9 Math Chapter – 12 Exercise – 12.1

NCERT Solution For Class 9 Math Chapter – 12 Exercise – 12.1

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Q1.

A traffic signal board indicating ‘SCHOOL AHEAD’ is an equilateral  triangle with side ‘a’ Find the area of the signal board using Heron ‘s Formula If its perimeter is 180 cm , what will be the area of the signal board?

Solution:-

Triangle is an equilateral triangle of side a.

S = a + a + a /2   = 3a/2

Using Heron Formula  we get

Area of triangle = √3a/2 (3a – a)(3a/a – a )(3a/2 – a)

= √3a/2 x a/2 x a/2 x a/2

= √3/4 a2

If perimeter = 180 cm , then side = 180/3

= 60 cm.

Area of triangle = √3/4 x (60)2

= 900√3 cm2.

Q2. The triangular side walls of a flyover have been used for advertisements The sides of the walls are 122 m , 22 m and 120 m The advertisements yield an earning of Rs 5000 per m2 per year A company  hired one of its walls for 3 months How much rent did it pay?

Solution:-

S = 122 + 120 + 22 / 2

S = 264/2

S = 132 m

Area = √(132)(132-122)(132-120)(132-22) m2.

= √132 x 10 x 12 x 110 m2.

= √11 x 12 x 10 x 12 x 11 x 10 m2

= 10 x 11 x 12 m2

Rent paid for 3 months = 1320 x 5000 x 3/12

= Rs 16,50,000.

Q3. There is a slide in a park One of its side wall has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN “ If the sides of the wall are 15 m 11 m and 6 m find the area painted in colour.

Solution:-

S = 15 + 11 + 6/2

S = 32/2

S = 16 m.

Area = √16(16-15)(16-11)(16-6)

= √16 x 1 x 5 x 10

= √800

= 20√2 m2.

Q4. Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.

Solution:-

S = 42/2

S = 21 cm

Area = √21(21-18)(21-10)(21-14)

= √21 x 3 x11 x 7

= 21√11 cm2.

Q5. Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm. Find its area.

Solution:-

12x + 17x + 25x = 540

54x = 540

X = 10

Therefore sides are 120 cm , 170 cm and 250 cm.

Semiperimeter = s = 540/2 = 270 cm

Applying Heron Formula we obtain

Area of the triangle = √270(270-120)(270-170)(270-250)

= √270x150x100x20

= √9x30x30x5x100x2x10

= 3 x 30 x 10 x 10

= 9000 cm2.

Q6. An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm Find the area of the triangle .

Solution:-

S = 12 + 12 + 6/2

S = 15

Area = √15(15-12)(15-12)(15-6)

= √15x3x3x9

= 9√15 cm2.