← Back to chapter
Vidaara.orgClass 9 · Mathematics
CodeVID-M9-12-CT
Heron's Formula — Full Chapter Test
Chapter: Heron's Formula
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • 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.
To find a quadrilateral's area, split it by a:
  • A.median
  • B.diagonal
  • C.midsegment
  • D.altitude
3.
Heron's formula: area $=$
  • A.$\sqrt{s(s-a)(s-b)(s-c)}$
  • B.$\tfrac12 bh$
  • C.$s(s-a)$
  • D.$abc$
4.
Heron's formula is useful when the ___ is unknown.
  • A.base
  • B.height
  • C.perimeter
  • D.a side
5.
Heron's formula needs the lengths of:
  • A.one side
  • B.all three sides
  • C.the height
  • D.two angles
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find $s$ for sides $5,6,7$.
7.
How do you apply Heron's formula to a quadrilateral?
8.
Find the area of a triangle with sides $3,4,5$.
9.
Find the area of an equilateral triangle of side $4$.
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 $9,12,15$ using Heron's formula.
12.
Find the area of a triangle with sides $5,12,13$.
13.
An isosceles triangle has equal sides $5$ cm and base $8$ cm. Find its area.
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 field $ABCD$ has $AB=9$ m, $BC=40$ m, $CD=15$ m, $DA=28$ m and $\angle B=90^\circ$. Find its area.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $\tfrac{a+b+c}{2}$
  2. (B) diagonal
  3. (A) $\sqrt{s(s-a)(s-b)(s-c)}$
  4. (B) height
  5. (B) all three sides
Section B — Short Answer (2 marks)
  1. $9$.
  2. Split it into two triangles by a diagonal and add their areas.
  3. $6$.
  4. $4\sqrt3$.
Section C — Short Answer (3 marks)
  1. $12\sqrt5$.
  2. $54$.
  3. $30$.
  4. $12$ cm$^2$.
Section D — Long Answer (5 marks)
  1. $84$ cm$^2$.
  2. $306$ m$^2$.
Generated by Vidaara.org · Assignment VID-M9-12-CT · vidaara.org