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SparkEd Math offers 60+ practice questions for Area of Plane Figures across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

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SparkEd Math uses visual step-by-step solutions for every Area of Plane Figures problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Area of Plane Figures content aligned with the ICSE syllabus?

Yes, all Area of Plane Figures questions and lessons on SparkEd Math are fully aligned with the Indian Certificate of Secondary Education (ICSE) syllabus for Class 9. The content follows the official curriculum structure and exam pattern.

Area of Plane Figures — Class 9 ICSE (2025-26)

About Area of Plane Figures — Class 9 ICSE

Calculate area of triangles using Heron's formula and area of quadrilaterals and polygons. This topic is part of the ICSE Class 9 mathematics syllabus (chapter: Chapter 17). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Area of Plane Figures

Introduction to Area of Plane Figures
Area of Triangles: Standard and Heron's Formula
Advanced Applications of Heron's Formula
Area of Quadrilaterals and Polygons
Summary, Connections, and Exam Preparation

Interactive lesson · about 15 minutes · checkpoint question after every unit

Area of Plane Figures — solved examples for Class 9 ICSE

Example 1easy

A triangular plot of land has sides measuring 13 m, 14 m, and 15 m. What is the area of the plot?

A)72 m²
B)84 m²
C)90 m²
D)100 m²

Step-by-step solution

First, calculate the semi-perimeter (s) of the triangle:
$s = (a + b + c) / 2 = (13 + 14 + 15) / 2 = 42 / 2 = 21 m$
Next, apply Heron's formula for the area (A):
$A = √[s(s-a)(s-b)(s-c)]$
Substitute the values:
$A = √[21(21-13)(21-14)(21-15)] = √[21 × 8 × 7 × 6]$
Simplify the expression:
$A = √[3 × 7 × 2³ × 7 × 2 × 3] = √[2⁴ × 3² × 7²] = 2² × 3 × 7 = 4 × 21 = 84 m²$

Answer: 84 m²

Example 2medium

A triangle has sides measuring 7 cm, 24 cm, and 25 cm. Using Heron's formula, calculate the area of this triangle.

A)84 cm²
B)105 cm²
C)150 cm²
D)210 cm²

Step-by-step solution

Given sides a = 7 cm, b = 24 cm, c = 25 cm.
Calculate the semi-perimeter (s): s = (a + b + c) / 2 = (7 + 24 + 25) / 2 = 56 / 2 = 28 cm.
Apply Heron's formula: Area = √(s(s-a)(s-b)(s-c))
Area = √(28 × (28-7) × (28-24) × (28-25)) = √(28 × 21 × 4 × 3) = √(7056) = 84 cm².

Answer: 84 cm²

Example 3hard

A triangular plot has sides in the ratio 3:4:5. If its perimeter is 144 meters, what is the area of the plot?

A)864 m²
B)960 m²
C)1728 m²
D)1152 m²

Step-by-step solution

Let the sides of the triangle be 3x, 4x, and 5x. The perimeter is 3x + 4x + 5x = 12x.
Given perimeter = 144 m, so 12x = 144, which means x = 12. The actual side lengths are 3×12 = 36 m, 4×12 = 48 m, and 5×12 = 60 m.
Since 36² + 48² = 1296 + 2304 = 3600 and 60² = 3600, the triangle satisfies the Pythagorean theorem (a² + b² = c²). Thus, it is a right-angled triangle.
The area of a right-angled triangle is (1/2) × base × height. Using the two shorter sides as base and height: Area = (1/2) × 36 m × 48 m = 18 × 48 m² = 864 m².

Answer: 864 m²

Practice questions on Area of Plane Figures

Q1.easy
Ravi was asked to find the area of a parallelogram with a base of 10 cm and a height of 6 cm. He calculated the area as 30 cm². What was Ravi's mistake?
1. A)He used the formula for the area of a triangle instead of a parallelogram.
2. B)He incorrectly multiplied the base and height.
3. C)He confused the height with a diagonal length.
4. D)He should have used Heron's formula for a parallelogram.
Show answer
Answer: He used the formula for the area of a triangle instead of a parallelogram.
Hint: Recall the correct formula for the area of a parallelogram and compare it with the formula for a triangle.
Q2.easy
Which of the following statements about the application of Heron's formula is TRUE?
1. A)Heron's formula can only be used for right-angled triangles.
2. B)Heron's formula requires the base and corresponding height of the triangle.
3. C)Heron's formula is applicable to any triangle, provided its three side lengths are known and form a valid triangle.
4. D)Heron's formula gives the perimeter of a triangle.
Show answer
Answer: Heron's formula is applicable to any triangle, provided its three side lengths are known and form a valid triangle.
Hint: Consider the primary purpose and input requirements for Heron's formula, and remember the conditions for forming a triangle.
Q3.easy
An isosceles triangle has a base of 12 cm and each of its equal sides is 10 cm. Which method would be MOST efficient to find its area?
1. A)Using Heron's formula directly.
2. B)First finding the height to the base, then using the formula (1/2) × base × height.
3. C)Assuming it's a right-angled triangle and using (1/2) × product of perpendicular sides.
4. D)Dividing it into two smaller triangles and using Heron's formula on each.
Show answer
Answer: First finding the height to the base, then using the formula (1/2) × base × height.
Hint: Consider the properties of an isosceles triangle and how a perpendicular from the vertex to the base behaves.
Q4.medium
The area of a parallelogram is 192 cm². If its base is 16 cm, what is the corresponding height of the parallelogram?
1. A)10 cm
2. B)12 cm
3. C)14 cm
4. D)16 cm
Show answer
Answer: 12 cm
Hint: Recall the formula for the area of a parallelogram. You are given the area and the base, and need to find the height.
Q5.medium
A rhombus has a perimeter of 52 cm. If one of its diagonals is 10 cm, what is the area of the rhombus?
1. A)60 cm²
2. B)80 cm²
3. C)100 cm²
4. D)120 cm²
Show answer
Answer: 120 cm²
Hint: First, find the side length of the rhombus from its perimeter. Then, use the property that diagonals of a rhombus bisect each other at right angles to find the length of the second diagonal.
Q6.medium
The parallel sides of a trapezium are 14 cm and 26 cm. If its area is 480 cm², what is the perpendicular distance between the parallel sides?
1. A)18 cm
2. B)20 cm
3. C)24 cm
4. D)30 cm
Show answer
Answer: 24 cm
Hint: Recall the formula for the area of a trapezium. You have the area and the lengths of the parallel sides, and need to find the height.
Q7.hard
An isosceles triangle has a perimeter of 36 cm. If the unequal side is 10 cm, what is its area?
1. A)48 cm²
2. B)60 cm²
3. C)72 cm²
4. D)84 cm²
Show answer
Answer: 60 cm²
Hint: Determine the length of the equal sides from the perimeter and the unequal side. Then, find the height to the unequal side using the Pythagorean theorem.
Q8.hard
A quadrilateral ABCD has BC = 12 cm, CD = 5 cm, AB = 10 cm and DA = 13 cm. If ∠C = 90°, what is the area of the quadrilateral?
1. A)80 cm²
2. B)90 cm²
3. C)100 cm²
4. D)110 cm²
Show answer
Answer: 90 cm²
Hint: Divide the quadrilateral into two triangles using diagonal BD. One of the triangles will be a right-angled triangle, simplifying its area calculation. Use the Pythagorean theorem to find the length of the diagonal, then Heron's formula for the other triangle.
Q9.hard
If the area of an equilateral triangle is 16√3 cm², what is its perimeter?
1. A)12 cm
2. B)16 cm
3. C)24 cm
4. D)32 cm
Show answer
Answer: 24 cm
Hint: Recall the formula for the area of an equilateral triangle in terms of its side. Use this to find the side length, then calculate the perimeter.

These are 9 of the 60 questions available for Area of Plane Figures. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.