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Heron's Formula Practice Problems with Solutions - CBSE Grade 9

CBSE Grade 9 | Math | Heron's Formula
Name: _________________________ Date: _________________________ Score: _______ / 40

A triangle of sides 3 cm, 4 cm and 5 cm has semi-perimeter 6 cm, and an equilateral triangle of side 6 cm has area 9√3 cm², so this Class 9 sheet opens by applying Heron's formulas to both triangle types. The key also records 6 cm² for a Heron area.

Key Takeaways

Section A: Multiple Choice Questions (1 Mark Each)

Choose the correct option for each question.
1. The semi-perimeter of a triangle whose sides are 3 cm, 4 cm and 5 cm is
(a) 5 cm(b) 6 cm(c) 7 cm(d) 12 cm
2. The area of an equilateral triangle of side 6 cm is
(a) 9√3 cm²(b) 6√3 cm²(c) 12√3 cm²(d) 18√3 cm²
3. The area of a right triangle with base 3 cm and height 4 cm is
(a) 6 cm²(b) 12 cm²(c) 24 cm²(d) 60 cm²
4. The area of an isosceles triangle with equal sides 5 cm and base 6 cm is
(a) 12 cm²(b) 15 cm²(c) 24 cm²(d) 30 cm²
5. For a triangle with sides a, b and c, the semi-perimeter s is given by
(a) (a + b + c)/2(b) a + b + c(c) (a + b + c)/3(d) (abc)/2
6. The perimeter of an equilateral triangle is 60 cm. Its area is
(a) 100√3 cm²(b) 200√3 cm²(c) 25√3 cm²(d) 50√3 cm²

Section B: Short Answer Type Questions (2 Marks Each)

Show all steps clearly.
7. Find the semi-perimeter of a triangle whose sides are 13 cm, 14 cm and 15 cm.
8. Write Heron's formula for the area of a triangle with sides a, b and c.
9. Find the area of an equilateral triangle of side 8 cm.
10. Find the area of a right triangle with base 6 cm and height 8 cm.
11. Find the semi-perimeter of a triangle whose sides are 10 cm, 10 cm and 12 cm.
12. State the situation in which Heron's formula is most useful.
13. Find the area of a triangle whose sides are 5 cm, 5 cm and 6 cm.
14. Two sides of a triangle are 8 cm each and its perimeter is 28 cm. Find the third side.

Section C: Numericals & Word Problems (3 Marks Each)

Apply the concepts to solve the problems. Show all working.
15. A park is in the shape of a triangle with sides 40 m, 24 m and 32 m. Find its area using Heron's formula.
16. The sides of a triangular field are 51 m, 37 m and 20 m. Find its area.
17. An equilateral triangle has a perimeter of 90 cm. Find its area.
18. A traffic signal board is an equilateral triangle of side 24 cm. Find its area.
19. Find the area of a triangle whose sides are 9 cm, 12 cm and 15 cm.
20. The base of an isosceles triangle is 24 cm and each of its equal sides is 13 cm. Find its area.

Answer Key

1. b) 6 cm
2. a) 9√3 cm²
3. a) 6 cm²
4. a) 12 cm²
5. a) (a + b + c)/2
6. a) 100√3 cm²
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet

People Also Ask

What is the semi-perimeter of a 3 cm, 4 cm, 5 cm triangle?

6 cm, option (b) in this worksheet (Q1).

What is the area of an equilateral triangle of side 6 cm?

9√3 cm², option (a) in this worksheet (Q2).

How is the semi-perimeter s defined?

(a + b + c)/2, option (a) in this worksheet (Q5).

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