Last reviewed: 11 November 2026
Updated November 2026. These Grade 7 area notes show the link between square metres and hectares, how to find the area of a rectangle, parallelogram, rhombus and trapezium, how to find the area of a circle, and how to find the area of a border or a combined shape. Area measures a surface. A school field that is 100 m by 50 m has area 5 000 m2, which is half a hectare.
The examples are original practice for Kenyan junior school learners, not an official paper. They follow the Grade 7 Mathematics measurements sub-strand on area in the KICD Grade Seven curriculum designs. Pentagons, hexagons and the surface area of pyramids, cones and spheres are Grade 9 work, in the Grade 9 area notes. For Grade 7 topics overall, use the Grade 7 mathematics revision guide and the Grade 7 notes hub.
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Square Metres, Hectares and the Main Plane Figures
1 hectare (ha) = 10 000 m2, the area of a square of side 100 m. So 2.5 ha = 25 000 m2, and 5 000 m2 = 0.5 ha. Acres also appear on some Kenyan land documents; the relationship the design asks you to identify clearly is the one between square metres and hectares.
The plane-figure formulas you need are collected below. They match the treatments in OpenStax Prealgebra’s section on rectangles, triangles and trapezoids.
| Figure | Area |
|---|---|
| Rectangle | length × width |
| Parallelogram | base × perpendicular height |
| Rhombus | (1/2) × product of the diagonals |
| Trapezium | (1/2) × (sum of the parallel sides) × height |
| Circle | πr2 |
Worked example: four plane figures
A rectangular noticeboard is 12 cm by 8 cm. Area = 12 × 8 = 96 cm2.
A parallelogram has base 10 cm and perpendicular height 6 cm. Area = 10 × 6 = 60 cm2. Do not multiply by a slanted side; the height must be perpendicular to the base.
A rhombus has diagonals 8 cm and 6 cm. Area = (1/2) × 8 × 6 = 24 cm2.
A trapezium has parallel sides 10 cm and 6 cm and height 4 cm. Area = (1/2) × (10 + 6) × 4 = 8 × 4 = 32 cm2.
Circles, Borders and Combined Shapes
The area of a circle is πr2. A useful classroom picture, used in the design, is to cut a circle into thin sectors and rearrange them into a shape that is almost a rectangle of sides r and πr. Borders and combined shapes are found by adding or subtracting the pieces you already know, the method also used in OpenStax Prealgebra’s section on circles and irregular figures.
Worked example: a circle and a border
A circular flower bed has radius 7 m. Taking π = 22/7, area = (22/7) × 49 = 154 m2.
A picture frame has outer measurements 12 cm by 10 cm and surrounds a photograph of 10 cm by 8 cm. Area of the border = 12 × 10 − 10 × 8 = 120 − 80 = 40 cm2.
A running track has a rectangular inner field 80 m by 40 m with a semicircle on each 40 m end, making one full circle of diameter 40 m. Area of the field-plus-ends = 80 × 40 + π × 202 = 3 200 + (22/7) × 400 = 3 200 + 8 800/7 = 3 200 + 1 257 1/7 = 4 457 1/7 m2.
Original Practice Questions With Worked Answers
- Convert 3 hectares to square metres. 30 000 m2.
- A rectangle is 15 m by 8 m. Find its area in hectares. 120 m2 = 0.012 ha.
- A parallelogram has base 14 cm and height 5 cm. Find its area. 70 cm2.
- A trapezium has parallel sides 9 cm and 5 cm and height 6 cm. Find its area. (1/2) × 14 × 6 = 42 cm2.
- A circle has diameter 14 cm. Taking π = 22/7, find its area. Radius 7 cm; area 154 cm2.
- A square lawn of side 10 m has a square pond of side 4 m in the middle. Find the grass area. 100 − 16 = 84 m2.
Cover the answers and try each question. Perimeter of the same figures is in the Grade 7 length notes. For timed practice use the Grade 7 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
How many square metres are in a hectare?
1 hectare = 10 000 m2, the area of a 100 m by 100 m square. A 100 m by 50 m field is therefore 0.5 ha.
How do you find the area of a trapezium?
Average the two parallel sides and multiply by the perpendicular height: (1/2)(a + b)h. Parallel sides 10 cm and 6 cm with height 4 cm give area 32 cm2.
How do you find the area of a border?
Subtract the inner area from the outer area. A 12 cm by 10 cm frame around a 10 cm by 8 cm photograph has a border of 40 cm2.
Which shapes are in Grade 7 area but not yet pyramids or spheres?
Grade 7 covers rectangles, parallelograms, rhombi, trapeziums, circles, borders and combined plane shapes, plus the hectare. Surface area of 3D solids such as pyramids and spheres is taught in Grade 9.
Get the marked answers for the Grade 7 Mathematics paper, KSh 20.
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