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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-12-HER-01
Heron's Formula - Assignment
Chapter: Heron's Formula
Topic: Heron's Formula for Area of a Triangle
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
The semi-perimeter $s=$
  • A.$a+b+c$
  • B.$\tfrac{a+b+c}{2}$
  • C.$\tfrac{a+b+c}{3}$
  • D.$abc$
2.
Heron's formula: area $=$
  • A.$\sqrt{s(s-a)(s-b)(s-c)}$
  • B.$\tfrac12 bh$
  • C.$s(s-a)$
  • D.$abc$
3.
Heron's formula needs the lengths of:
  • A.one side
  • B.all three sides
  • C.the height
  • D.two angles
4.
For sides $3,4,5$, $s=$
  • A.$6$
  • B.$12$
  • C.$5$
  • D.$7$
5.
The area of a $3,4,5$ triangle is:
  • A.$5$
  • B.$6$
  • C.$12$
  • D.$10$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find $s$ for sides $5,6,7$.
7.
Find the area of a triangle with sides $3,4,5$.
8.
State Heron's formula.
9.
Find $s$ for an equilateral triangle of side $6$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the area of a triangle with sides $7,8,9$.
11.
Find the area of a triangle with sides $5,12,13$.
12.
Find the area of an equilateral triangle of side $6$ using Heron's formula.
13.
Find the area of a triangle with sides $6,8,10$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Find the area of a triangle with sides $13$ cm, $14$ cm and $15$ cm using Heron's formula.
15.
A triangular park has sides $40$ m, $24$ m and $32$ m. Find its area and the cost of levelling at $\textsf{Rs }5$ per m$^2$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $\tfrac{a+b+c}{2}$
  2. (A) $\sqrt{s(s-a)(s-b)(s-c)}$
  3. (B) all three sides
  4. (A) $6$
  5. (B) $6$
Section B — Short Answer (2 marks)
  1. $9$.
  2. $6$.
  3. Area $=\sqrt{s(s-a)(s-b)(s-c)}$.
  4. $9$.
Section C — Short Answer (3 marks)
  1. $12\sqrt5$.
  2. $30$.
  3. $9\sqrt3$.
  4. $24$.
Section D — Long Answer (5 marks)
  1. $84$ cm$^2$.
  2. Area $384$ m$^2$; cost $\textsf{Rs }1920$.
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