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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-12-APP-01
Application of Heron's Formula - Assignment
Chapter: Heron's Formula
Topic: Application of Heron's Formula in Real-Life Contexts
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.
To find a quadrilateral's area, split it by a:
  • A.median
  • B.diagonal
  • C.midsegment
  • D.altitude
2.
Heron's formula is useful when the ___ is unknown.
  • A.base
  • B.height
  • C.perimeter
  • D.a side
3.
A quadrilateral's area $=$ sum of areas of:
  • A.its sides
  • B.two triangles
  • C.its diagonals
  • D.its angles
4.
Heron's formula uses only the:
  • A.angles
  • B.side lengths
  • C.height
  • D.diagonals
5.
For an equilateral triangle of side $a$, area $=$
  • A.$\tfrac{\sqrt3}{4}a^2$
  • B.$a^2$
  • C.$\tfrac12a^2$
  • D.$\sqrt3 a$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
How do you apply Heron's formula to a quadrilateral?
7.
Find the area of an equilateral triangle of side $4$.
8.
Heron's formula is helpful when which measurement is missing?
9.
Find $s$ for a triangle with sides $9,12,15$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the area of a triangle with sides $9,12,15$ using Heron's formula.
11.
An isosceles triangle has equal sides $5$ cm and base $8$ cm. Find its area.
12.
Find the area of an equilateral triangle of side $11$.
13.
A triangular field has sides $50,50,80$ m. Find its area.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A field $ABCD$ has $AB=9$ m, $BC=40$ m, $CD=15$ m, $DA=28$ m and $\angle B=90^\circ$. Find its area.
15.
Find the area of an isosceles triangle of perimeter $32$ cm whose equal sides are $10$ cm each.

Answer Key

Section A — Multiple Choice Questions
  1. (B) diagonal
  2. (B) height
  3. (B) two triangles
  4. (B) side lengths
  5. (A) $\tfrac{\sqrt3}{4}a^2$
Section B — Short Answer (2 marks)
  1. Split it into two triangles by a diagonal and add their areas.
  2. $4\sqrt3$.
  3. The height.
  4. $18$.
Section C — Short Answer (3 marks)
  1. $54$.
  2. $12$ cm$^2$.
  3. $\tfrac{121\sqrt3}{4}$.
  4. $1200$ m$^2$.
Section D — Long Answer (5 marks)
  1. $306$ m$^2$.
  2. $48$ cm$^2$.
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