# HERON’S FORMULA NCERT 9 MATHEMATICS TEXTBOOK MCQ (Multiple Choice Questions)

Q1. The lengths of a triangle are 6 cm, 8 cm and 10 cm. Then the length of perpendicular from the opposite vertex to the side whose length is 8 cm is:

1. 5 cm
2. 4 cm
3. 2 cm
4. 6 cm

Q2. The perimeter of a right triangle is 144 cm and its hypotenuse measures 65 cm. The other sides and its area are

1. 26 cm, 63 cm, 504 cm2
2. 16 cm, 63 m , 604 cm2
3. 16 cm, ,63 cm, 504 cm2
4. 16 cm , 68 cm, 504 cm2

Q3. The area of a triangle with two equal sides of length 12 cm making a right angle is

1. 72 cm2
2. 42 cm2
3. 23 cm2
4. 32 cm2

Q4. The area of a right triangle with base 5 m and altitude 12 m is

1. 9 m2
2. 30 m2
3. 15 m2
4. 50 m2

Q5. A square sheet whose perimeter is 32 cm is painted at the rate of Rs. 5 per m2. The cost of painting is:

1. Rs. 320
2. Rs. 340
3. Rs. 350
4. Rs. 160

Q6. The area of an equilateral triangle of side 14 cm is

1. 18 cm2
2. 49√3 cm2
3. 56√3 cm
4. 58√3 cm2

Q7. The area of a triangle, two sides of which are 5 cm and 6 cm and perimeter is 16 cm is

1. 36 cm2
2. 18 cm2
3. 42 cm2
4. 12 cm2

Q8. The sides of a triangle are in the ratio of 13 : 14 : 15 and its perimeter is 84 cm. The area of the triangle will be equal to

1. 836 cm2
2. 386 cm2
3. 336 cm2
4. 886 cm2

Q9. The area of a right triangle of height 15 m and base 20 m is

1. 160 m2
2. 216 m2
3. 150 m2
4. 210 m2

Q10. Sides of a triangle are in the ratio of 4 : 6 : 7 and its perimeter is 340 cm. its area is

1. 300 cm2
2. 300√255 cm2
3. 100√255 cm2
4. 4800 cm2

Q11. The perimeter of a rhombus is 146 cm. One of its diagonals is 55 cm. The length of the other diagonal and area of the rhombus are

1. 48 cm, 2320 cm2
2. 48 cm, 1320 cm2
3. 88 cm, 1320 cm2
4. 48 cm, 1820 cm2

Q12. Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on land and produce different crops to suffice the needs of their family. She divided the land in two equal parts. If the perimeter of the land is 400 m and one of the diagonals is 160 m, the area of each part is

1. 4800 m2
2. 8800 m2
3. 48000 m2
4. 480 m2

Q13. The base of an isosceles triangle is 10 cm and one of its equal sides is 13 cm. The area of the triangle is

1. 50 cm2.
2. 60 cm2
3. 80 cm2
4. 100 cm2

Q14. The lengths of a triangle are 6 cm, 8 cm and 10 cm. Then the length of perpendicular from the opposite vertex to the side whose length is 8 cm is:

1. 5 cm
2. 4 cm
3. 6 cm
4. 2 cm

Q15. The area of a triangle with sides 32 cm, 34 cm and 34 cm is

1. 316 cm2
2. 382 cm2
3. 548 cm2
4. 480 cm2

Q16. The triangular side walls of a fly-over have been used for advertisements. The sides of the walls are 122m, 22m and 120m. The advertisements yield an earning of Rs. 5000 per m2 per year. A company hired one of its walls for 3 months. The rent paid by the company is

1. Rs. 165000
2. Rs. 1550000
3. Rs. 16500000
4. Rs. 1650000

Q17. The area of a triangle, two sides of which are 15 cm and 18 cm and perimeter is 48 cm is

1. 112 cm2
2. 108 cm2
3. 98 cm2
4. 86 cm2

Q18. The adjacent sides of a parallelogram PQRS measure 34 cm and 20 cm and the diagonal QS measures 42 cm. Then, the area of parallelogram is:

1. 924 cm2
2. 672 cm2
3. 545 cm2
4. 850 cm2

Q19. The perimeter of a triangle with two sides of length 15 cm and 12.5 cm is 40 cm. Find the area of the triangle.

1. 12 cm2
2. 75 cm2
3. 45 cm2
4. 35 cm2

Q20. The sum of length, breadth and height of a cuboidal box is 19 cm and the length of its diagonal is 11 cm. find the surface area of the cuboidal box.

1. 240 cm2
2. 315 cm2
3. 451 cm2
4. 512 cm2

Q21. The area of quadrilateral PQRS, in which PQ = 7 cm, QR = 6 cm, RS = 12 cm, PS = 15 cm and PR = 9 cm:

1. 68.25 cm2
2. 25.25 cm2
3. 75 cm2
4. 74.98 cm2

Q22. The area of a triangle with sides 37.5 cm, 37.5 cm and 45 cm and semi-perimeter 60 cm is

1. 625 cm2
2. 675 cm2
3. 525 cm2
4. 575 cm2

Q23. If the radius of its circumcircle is 5 cm and the altitude drawn to the hypotenuse is 4 cm, the area of a right-angled triangle is equal to

1. 20 cm2
2. 50 cm2
3. 40 cm2
4. 10 cm2

Q24. The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m. Its area is

1. 8598. 08m2
2. 6598. 08m2
3. 2598. 08m2
4. 5598. 08m2

Q25. A carpenter had to make a triangle with sides 5, 6, 5 units. By mistake he made one with sides 5, 8, 5 units. The difference between their areas is:

1. 16 sq units
2. 4 sq units
3. 2 sq units
4. 0 sq units

Q26. The base of a right angled triangle with area 300 cmand height 30 cm is

1. 15 cm
2. 30 cm
3. 20 cm
4. 10 cm

Q27. A square sheet whose perimeter is 32 cm is painted at the rate of Rs. 5 per cm2. The cost of painting is:

1. Rs.500
2. Rs.320
3. Rs.640
4. Rs.550

Q28. The area of an isosceles triangle is 60 cm2 and the length  of each one of its equal sides is 13 cm, the length of  its base is

1. 14 cm, or 10 cm
2. 24 cm, or 10 cm
3. 24 cm, or 20 cm
4. 44 cm, or 10 cm

Q29. The sides of a triangle are in the ratio 25 : 17 : 12 and its perimeter is 540 m. The area of the triangle is

1. 9000 m2
2. 10000 m2
3. 12000 m2
4. 5000 m2

Q30. The perimeter of an isosceles right angled triangle having an area of 200 cm2 is

1. 88.2 cm
2. 68.5 cm
3. 69.2 cm
4. 68.2 cm.

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