How many practice questions are available for Area & Perimeter?

SparkEd Math offers 48+ practice questions for Area & Perimeter 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 Area & Perimeter content free on SparkEd Math?

Yes! All Area & Perimeter 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 Area & Perimeter differently from textbooks?

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

Yes, all Area & Perimeter questions and lessons on SparkEd Math are fully aligned with the International Baccalaureate (MYP) (IB) syllabus for Class 7. The content follows the official curriculum structure and exam pattern.

Area & Perimeter — Class 7 IB (2025-26)

About Area & Perimeter — Class 7 IB

Calculate area and perimeter of composite shapes including circles and irregular figures. This topic is part of the IB Class 7 mathematics syllabus (chapter: Unit 7). On this page you can practice 48 questions across three difficulty levels — 10 easy, 19 medium, and 19 hard — each with a visual step-by-step solution, plus a timed 33-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Area & Perimeter

Unveiling Area and Perimeter: What are they and why do they matter?
Mastering Basic Shapes: Rectangles, Triangles, Parallelograms, and Trapeziums
Embracing Curves: Circles – Circumference and Area
Beyond Basic: Perimeter of Composite Shapes
Strategic Thinking: Area of Composite Shapes & Problem Solving

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

Area & Perimeter — solved examples for Class 7 IB

Example 1easy

A rectangular swimming pool in a Berlin park has a length of 15.5 metres and a width of 8 metres. If a safety rope needs to be placed around the entire perimeter of the pool, what length of rope is required?

A)23.5 metres
B)47 metres
C)124 metres
D)94 metres

Step-by-step solution

Identify the given dimensions: Length = 15.5 m, Width = 8 m.
Apply the perimeter formula for a rectangle: Perimeter = 2 × (Length + Width).
$P = 2 × (15.5 + 8)$
Calculate the sum of length and width: 15.5 + 8 = 23.5 m.
Multiply by 2: 2 × 23.5 = 47 m.

Answer: 47 metres

Example 2medium

A gardener is designing a new flower bed shaped like an 'L'. The overall length of the 'L' is 8 meters and the overall width is 6 meters. The cutout section is a rectangle measuring 3 meters by 2 meters. If the gardener wants to put an edging around the entire flower bed, what total length of edging will be needed?

A)22 m
B)28 m
C)30 m
D)34 m

Step-by-step solution

Identify the known outer dimensions: Length = 8 m, Width = 6 m. The cutout is 3 m by 2 m.
The perimeter of an L-shape can be found by adding all its outer sides. The 'hidden' inner sides correspond to the dimensions of the cutout. The total perimeter is (8 + 6 + 5 + 3 + 3 + 3) m. Alternatively, for a rectilinear L-shape, the perimeter is equivalent to the perimeter of the enclosing rectangle if the inner dimensions match the outer differences. (8 + 6) × 2 = 28 m.
The outer perimeter is 8 m + 6 m + (8-3) m + 2 m + 3 m + (6-2) m = 8 + 6 + 5 + 2 + 3 + 4 = 28 m.
The total length of edging required is 28 meters.

Answer: 28 m

Example 3hard

A rectangular sheet of metal measures 20 cm by 15 cm. A rectangular notch, 10 cm long and 10 cm wide, is cut out from the middle of one of the 20 cm sides, extending inwards. All cuts are straight and parallel/perpendicular to the original sides. What is the perimeter of the resulting shape?

A)60 cm
B)70 cm
C)80 cm
D)90 cm

Step-by-step solution

Calculate the perimeter of the original rectangle: P_original = 2 × (20 + 15).
$P_original = 2 × 35 = 70 cm$
When a 10 cm × 10 cm rectangular notch is cut from the middle of a 20 cm side, the 10 cm segment of the original side is removed.
This removed 10 cm segment is replaced by three new segments: two segments of 10 cm (the depth of the cut) and one segment of 10 cm (the width of the cut). The new total length added is 10 + 10 + 10 cm.
$Added length = 30 cm$
The net change to the perimeter is the added length minus the removed length. The perimeter of the resulting shape is P_new = P_original + (Added length - Removed length).
$P_new = 70 + (30 - 10) = 70 + 20 = 90 cm$

Answer: 90 cm

Practice questions on Area & Perimeter

Q1.easy
A classroom floor in Sydney, Australia, is a rectangle with a length of 9.2 metres and a width of 7 metres. What is the area of the floor? (Give your answer in square metres)
1. A)16.2 m²
2. B)32.4 m²
3. C)64.4 m²
4. D)63.4 m²
Show answer
Answer: 64.4 m²
Hint: To find the area of a rectangle, you multiply its length by its width.
Q2.easy
Alex was asked to find the area of a square with a side length of 6 cm. He wrote down the following steps:

Step 1: Area = side + side
Step 2: Area = 6 cm + 6 cm
Step 3: Area = 12 cm²

Which statement correctly identifies Alex's mistake?
1. A)Alex's calculation in Step 2 is incorrect.
2. B)Alex used the formula for perimeter instead of area in Step 1.
3. C)The units in Step 3 should be 'cm' not 'cm²'.
4. D)The answer should be 36 cm², so his final calculation is wrong.
Show answer
Answer: Alex used the formula for perimeter instead of area in Step 1.
Hint: Recall the correct formula for the area of a square. Area involves multiplication of dimensions, not addition.
Q3.easy
A triangular sail on a yacht has a base of 4 metres and a perpendicular height of 6.5 metres. What is the area of the sail?
1. A)13 m²
2. B)10.5 m²
3. C)21 m²
4. D)26 m²
Show answer
Answer: 13 m²
Hint: The area of a triangle is half the product of its base and its perpendicular height.
Q4.medium
A conservation team is planning to re-wild a rectangular plot of land in the Scottish Highlands. The plot measures 2.5 km by 1.2 km. What is the total area of land to be re-wilded?
1. A)3 km²
2. B)3.7 km²
3. C)3.0 km²
4. D)4.2 km²
Show answer
Answer: 3.0 km²
Hint: Recall the formula for the area of a rectangle. Pay close attention to the decimal multiplication.
Q5.medium
Consider a triangular sail on a yacht. If its base is 4.8 meters and its perpendicular height is 7.5 meters, what is the area of material needed for the sail?
1. A)18 m²
2. B)36 m²
3. C)12.3 m²
4. D)24 m²
Show answer
Answer: 18 m²
Hint: Remember the specific formula for the area of a triangle, which involves its base and perpendicular height.
Q6.medium
A designer is creating a pattern using parallelogram-shaped tiles. Each tile has a base of 18 cm and a perpendicular height of 10 cm. If they use one such tile, what area does it cover?
1. A)90 cm²
2. B)180 cm²
3. C)28 cm²
4. D)360 cm²
Show answer
Answer: 180 cm²
Hint: The area of a parallelogram is found by multiplying its base by its perpendicular height.
Q7.hard
A plot of land in the Swiss Alps is shaped like a trapezium. Its area is 240 m². One parallel side measures 18 m, and the height of the trapezium is 12 m. What is the length of the other parallel side?
1. A)12 m
2. B)15 m
3. C)22 m
4. D)28 m
Show answer
Answer: 22 m
Hint: Start with the formula for the area of a trapezium and substitute the known values. Then, work backwards to solve for the unknown side.
Q8.hard
A rectangular window pane in a Parisian apartment measures 100 cm in length and 80 cm in width. A decorative, quarter-circular section with a radius of 20 cm is cut out from one of its corners. What is the remaining area of the window pane? (Use π ≈ 3.14)
1. A)7858 cm²
2. B)7686 cm²
3. C)7500 cm²
4. D)7458 cm²
Show answer
Answer: 7686 cm²
Hint: First, find the total area of the rectangle. Then, calculate the area of the quarter-circular section and subtract it from the total.
Q9.hard
An artist is creating a triangular support structure for an installation in Berlin. The triangular face has a base of 30 cm. The height of the triangle is equal to half the side length of a square whose perimeter is 40 cm. What is the area of this triangular face?
1. A)75 cm²
2. B)37.5 cm²
3. C)150 cm²
4. D)60 cm²
Show answer
Answer: 75 cm²
Hint: First, determine the side length of the square from its perimeter. Then, use this to find the height of the triangle before calculating its area.

These are 9 of the 48 questions available for Area & Perimeter. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.