How many practice questions are available for Perimeter and Area?

SparkEd Math offers 60+ practice questions for Perimeter and Area 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.

Is Perimeter and Area content free on SparkEd Math?

Yes! All Perimeter and Area content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Perimeter and Area differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Perimeter and Area 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 Perimeter and Area content aligned with the Olympiad syllabus?

Yes, all Perimeter and Area questions and lessons on SparkEd Math are fully aligned with the Mathematical Olympiad Preparation (Olympiad) syllabus for Class 7. The content follows the official curriculum structure and exam pattern.

Perimeter and Area — Class 7 Olympiad (2025-26)

About Perimeter and Area — Class 7 Olympiad

Calculate perimeter and area of triangles, quadrilaterals, and circles; solve composite figure challenges. This topic is part of the Olympiad Class 7 mathematics syllabus (chapter: Module 10). On this page you can practice 58 questions across three difficulty levels — 18 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.

Perimeter and Area — solved examples for Class 7 Olympiad

Example 1easy

A wire of length 48 cm is bent to form a square. If the same wire is re-bent to form a rectangle of length 14 cm, what will be the difference in the areas of the square and the rectangle?

A)4 cm²
B)9 cm²
C)16 cm²
D)25 cm²

Step-by-step solution

For the square: Perimeter = 48 cm. Side of square = 48 cm / 4 = 12 cm. Area of square = side × side = 12 cm × 12 cm = 144 cm².
For the rectangle: Perimeter = 48 cm. Length = 14 cm. Perimeter = 2 × (Length + Breadth). So, 48 = 2 × (14 + Breadth). 24 = 14 + Breadth. Breadth = 24 - 14 = 10 cm.
Area of rectangle = Length × Breadth = 14 cm × 10 cm = 140 cm².
Difference in areas = Area of square - Area of rectangle = 144 cm² - 140 cm² = 4 cm².

Answer: 9 cm²

Example 2medium

A rectangle ABCD has length AB = 12 cm and width BC = 8 cm. Point P is the midpoint of side AB, and point Q is the midpoint of side BC. What is the area of triangle DPQ?

A)32 cm²
B)36 cm²
C)40 cm²
D)48 cm²

Step-by-step solution

The total area of the rectangle ABCD is length × width = 12 cm × 8 cm = 96 cm².
P is the midpoint of AB, so AP = PB = 12/2 = 6 cm. Q is the midpoint of BC, so BQ = QC = 8/2 = 4 cm.
Area of triangle ADP = (1/2) × base AP × height AD = (1/2) × 6 cm × 8 cm = 24 cm².
Area of triangle BPQ = (1/2) × base PB × height BQ = (1/2) × 6 cm × 4 cm = 12 cm².
Area of triangle CDQ = (1/2) × base CD × height CQ = (1/2) × 12 cm × 4 cm = 24 cm².
The area of triangle DPQ is the area of the rectangle minus the sum of the areas of the three surrounding triangles: 96 cm² - (24 cm² + 12 cm² + 24 cm²) = 96 cm² - 60 cm² = 36 cm².

Answer: 36 cm²

Example 3hard

How many distinct rectangles exist such that their side lengths are positive integers and their area is numerically equal to their perimeter?

A)(A) 1
B)(B) 2
C)(C) 3
D)(D) 4

Step-by-step solution

Let the length be L and width be W. The given condition is LW = 2(L+W).
Rearrange the equation: LW - 2L - 2W = 0. Add 4 to both sides: LW - 2L - 2W + 4 = 4.
Factor by grouping: L(W-2) - 2(W-2) = 4, which simplifies to (L-2)(W-2) = 4.
Since L and W are positive integers, (L-2) and (W-2) must be integer factors of 4. Possible pairs for (L-2, W-2) are (1,4), (4,1), and (2,2). These yield (L,W) pairs as (3,6), (6,3), and (4,4). Considering distinct rectangles (3x6 is the same as 6x3), there are 2 distinct rectangles: 3x6 and 4x4.

Answer: (B) 2

Practice questions on Perimeter and Area

Q1.easy
A rectangular sheet of paper has a length of 20 cm and a width of 15 cm. A triangular piece is cut from one corner such that its base is 8 cm and its height is 6 cm (along the sides of the rectangle). What is the area of the remaining paper?
1. A)252 cm²
2. B)260 cm²
3. C)276 cm²
4. D)282 cm²
Show answer
Answer: 276 cm²
Hint: First, calculate the total area of the rectangular sheet. Then, find the area of the triangular piece that was removed.
Q2.easy
A bicycle wheel has a diameter of 70 cm. How many revolutions will it make to cover a distance of 1.1 km? (Take π = 22/7)
1. A)500
2. B)550
3. C)600
4. D)1000
Show answer
Answer: 500
Hint: One revolution covers a distance equal to the circumference of the wheel. Remember to convert all units to be consistent.
Q3.easy
The area of a triangular field is 1200 m². If its base is 60 m, what is the height corresponding to this base?
1. A)20 m
2. B)30 m
3. C)35 m
4. D)40 m
Show answer
Answer: 40 m
Hint: Recall the formula for the area of a triangle. You'll need to work backward to find the height.
Q4.medium
A square of side 10 cm has a smaller square of side 2 cm cut out from one of its corners, as shown in the figure (imagine a corner removed). What is the perimeter of the remaining shape?
1. A)40 cm
2. B)36 cm
3. C)44 cm
4. D)48 cm
Show answer
Answer: 40 cm
Hint: Carefully trace the new boundary. Notice how cutting a square from a corner affects the lengths of the sides.
Q5.medium
A rhombus has diagonals in the ratio 3:4. If its area is 96 cm², what is the sum of the lengths of its diagonals?
1. A)24 cm
2. B)28 cm
3. C)32 cm
4. D)36 cm
Show answer
Answer: 28 cm
Hint: Recall the formula for the area of a rhombus in terms of its diagonals. Let the diagonals be 3x and 4x.
Q6.medium
A circular wheel of radius 14 cm makes 250 revolutions to cover a certain distance. What is the distance covered in kilometers? (Use π = 22/7)
1. A)0.11 km
2. B)0.18 km
3. C)0.22 km
4. D)0.25 km
Show answer
Answer: 0.22 km
Hint: First, calculate the circumference of the wheel. The total distance is the circumference multiplied by the number of revolutions, then convert units.
Q7.hard
In triangle ABC, D is a point on BC such that BD:DC = 1:2. E is a point on AC such that AE:EC = 1:3. If the area of triangle ABC is 72 cm², what is the area of triangle BDE?
1. A)(A) 12 cm²
2. B)(B) 16 cm²
3. C)(C) 18 cm²
4. D)(D) 24 cm²
Show answer
Answer: (C) 18 cm²
Hint: Use the property that if two triangles share the same height, the ratio of their areas is equal to the ratio of their bases.
Q8.hard
A parallelogram has a perimeter of 80 cm. The ratio of the lengths of its adjacent sides is 3:5. If the altitude corresponding to the longer side is 12 cm, what is the area of the parallelogram?
1. A)(A) 180 cm²
2. B)(B) 240 cm²
3. C)(C) 300 cm²
4. D)(D) 360 cm²
Show answer
Answer: (C) 300 cm²
Hint: Use the perimeter and side ratio to find the actual lengths of the sides first. Then apply the area formula for a parallelogram.
Q9.hard
A circular wire of radius 'r' is bent to form a square. What is the ratio of the area of the square to the area of the original circle?
1. A)(A) 4/π
2. B)(B) π/4
3. C)(C) 4/(π²)
4. D)(D) π/(4π)
Show answer
Answer: (B) π/4
Hint: The length of the wire remains constant. Equate the circumference of the circle to the perimeter of the square.

These are 9 of the 58 questions available for Perimeter and Area. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.