Mensuration (Perimeter and Area of Plane Figures)
ICSE Class 7 · Mathematics · Chapter 20
What this chapter covers
- Perimeter of plane figures
- Circumference of a circle
- Area and the area of a square and a rectangle
- Area of a parallelogram
- Area of a triangle
- Area of a circle and of a ring
- Area and perimeter of combined figures
Key points
- Perimeter is the length of the boundary of a closed figure; it is measured in units of length.
- Perimeter of a rectangle = 2(l + b); perimeter of a square = 4s.
- Circumference of a circle = π d = 2π r, with π ≈ (22)/(7) or 3.14.
- Area is the surface enclosed by a figure; it is measured in square units.
- 1 m2 = 10000 cm2 and 1 cm2 = 100 mm2.
- Area of a rectangle = l × b; area of a square = s2.
- Area of a parallelogram = base × perpendicular height.
- Area of a triangle = (1)/(2) × base × height.
- Area of a circle = π r2; area of a ring = π (R2 - r2).
- For a combined figure, split it into simple shapes, then add or subtract their areas; count only the outer edge for its perimeter.
Questions answered
A rectangular field is 23 m long and 17 m wide. Find its perimeter.
2(23 + 17) = 80 m.
Explain why two figures with the same perimeter need not have the same area.
Perimeter measures only the boundary. A 9 cm by 1 cm rectangle and a 5 cm square both have perimeter 20 cm, but their areas are 9 cm2 and 25 cm2.
Find the circumference of a circle of diameter 21 cm. (Take π = (22)/(7).)
(22)/(7) × 21 = 66 cm.
The circumference of a wheel is 132 cm. Find its radius. (Take π = (22)/(7).)
2 × (22)/(7) × r = 132, so r = 21 cm.
A square has a perimeter of 36 cm. Find its area.
Side = 9 cm, so area = 81 cm2.
Express 3.5 m2 in square centimetres.
3.5 × 10000 = 35000 cm2.
Find the area of a parallelogram with base 16 cm and height 5 cm.
16 × 5 = 80 cm2.
A triangle has base 10 m and height 7 m. Find its area.
(1)/(2) × 10 × 7 = 35 m2.