Perimeter, circles and composite figures
Work out the perimeter of any polygon and L-shape, find the area of composite figures, and learn the radius, diameter and circumference of a circle. Read one step, play with it, then tap “I understand this”.
Perimeter: walk around the edge
The perimeter is the distance all around a shape: add all the sides together. It is a length, so the unit is cm or m (not cm²).
Rectangle: P = 2 × (l + b) · Square: P = 4 × s · Regular polygon: P = number of sides × s
Perimeter builder
Choose a shape and change the sides.
The perimeter of an L-shape
In a composite figure some sides are often missing. Look at the opposite side: the pieces at the top add up to the whole bottom, and the pieces on the right add up to the whole left side.
Find a and b
Change the figure. Watch how a and b are worked out, and what happens to the perimeter.
Do you see the shortcut? When you cut out a corner, the two sides just move inwards. The L-shape has the same perimeter as the big rectangle.
When you cut out a corner, the two sides of that corner just move inwards. They are still the same length, so the path around the figure is no longer or shorter.
The area of a composite figure
Area is the space inside the figure, in cm². Cut the figure into rectangles (A + B), or work out the big rectangle and subtract the piece that is missing.
Two ways
Choose a way and change the figure. Both must give the same answer.
Perimeter is cm (around the edge), area is cm² (inside). Do not mix the two up.
The circle: radius, diameter and circumference
- The centre is exactly in the middle. Every point on the circle is the same distance from it.
- The radius (r) goes from the centre to the edge. The diameter (d) goes right through the centre: d = 2 × r.
- The circumference of a circle is about 3,14 times the diameter: C = π × d. We use π ≈ 3,14.
The circle
Change the radius and roll the circle out.
Try it yourself: wrap a string around a tin and measure the string. Divide it by the diameter of the tin. You get almost 3,14!
Thousands of years ago people already noticed that the circumference of every circle, big or small, is about 3,14 times its diameter. That number got the name π (pi).
Play: perimeter, area and circles
What is the answer?
Choose the right answer. Look carefully at the unit.
Correct: 0Check yourself
- Perimeter = all the sides added (cm). Rectangle: P = 2 × (l + b).
- L-shape: find the missing sides from the opposite side. The perimeter is the same as the big rectangle’s.
- Composite area (cm²): cut into rectangles, or big rectangle minus the missing piece.
- Circle: d = 2 × r and circumference C = π × d ≈ 3,14 × d.
Write these points in your maths book. Read them again the night before the test.
Quick questions
Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.
You ticked all 5 steps! Now you are ready for the quiz.- Practice sheet for this classQuestions + memo · 3 A4 pagesPractice sheet
- Measurement6 pages · PDFPaperMemo
- Geometry8 pages · PDFPaperMemo
Ready for more? The Grade 7 quiz on perimeter, circles and composite figures gives you new questions every time.
- One step a day is enough. Ten calm minutes work better than an hour the night before the test.
- Measure the diameter and circumference of a plate, a tin and a wheel together with a string and a tape measure. Divide circumference by diameter each time.
- Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
- The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.
Follows CAPS for Grade 7 Maths. Always check your teacher’s notes and textbook too.