Grade 9 Area: Short Notes

9 ශ්‍රේණිය · 23 පරිච්ඡේදය · වර්ගඵලය

68%

of Grade 9 term tests include it (27 of 40)

309

marks in past papers (48 questions)

10 min

full lesson with quick checks

🎯 What you'll learn

Find the area of a parallelogram
Find the area of a trapezium
Find the area of a circle and a semicircle
Find areas of composite shapes and missing lengths
Tell area from perimeter and use square units

How much seed paddy?

A farmer in Ampara has a paddy field shaped like a trapezium, and a round pond for watering buffaloes. To buy the right amount of seed paddy and fertiliser, he needs the area of each. Rectangles are easy; these shapes need three new formulas.

Area, not perimeter

Area is the amount of flat surface inside a shape, measured in square units: cm², m².Perimeter is the distance around the edge, measured in cm or m.You already know: rectangle = length × breadth, triangle = ½ × base × height. Each new formula below is built from these.

Parallelogram: A = b × h

Cut off the blue triangle and slide it to the other end. The parallelogram becomes a rectangle with the same base b and height h. So area = base × perpendicular height.

✏️ A parallelogram tile

A floor tile is a parallelogram with base 12 cm, perpendicular height 7 cm and slanting side 8 cm. Find its area.

1Area = base × perpendicular height.
2= 12 × 7 = 84 cm². The 8 cm side is not needed.

✅ 84 cm²

⚠️ The slanting side is not the height

For the tile, 12 × 8 = 96 cm² is wrong. The height must be perpendicular to the base: look for the dashed line with a right-angle mark. The slanting side is always longer than the height, so using it gives too big an area.

Trapezium: two triangles

A diagonal splits the trapezium into two triangles with the same height h: one with base a, one with base b. Area = ½ah + ½bh = ½(a + b)h.

🧮 Area of a trapezium

a and b are the two parallel sides and h is the perpendicular distance between them. In words: half the sum of the parallel sides, times the distance between them.

A = ½ × (a + b) × h

✏️ The paddy field

The Ampara paddy field is a trapezium. Its parallel sides are 18 m and 12 m, and they are 10 m apart. Find its area.

1Add the parallel sides: 18 + 12 = 30 m.
2Area = ½ × 30 × 10 = 150 m².

✅ 150 m²

Circle: unroll the slices

Cut a circle into equal slices and lay them top-to-tail. They make a shape close to a rectangle: its length is half the circumference, πr, and its height is r. So the area is πr × r = πr².

🧮 Area of a circle

r is the radius. If you are given the diameter, halve it first. Use 22/7 when the radius is a multiple of 7; otherwise use 3.14, or whatever value the question gives.

A = πr² (π ≈ 22/7 or 3.14)

⚠️ Area or perimeter? cm or cm²?

In O/L papers many candidates found the perimeter when the area was asked: for a square of side 5, they gave 20 instead of 25. Others dropped the units. Read the question twice; area answers are always in square units. And for circles, check whether you were given the radius or the diameter.

📌 Remember

• Parallelogram: A = base × perpendicular height.• Trapezium: A = ½ × (sum of parallel sides) × height.• Circle: A = πr²; halve the diameter first.• Composite shapes: split into known shapes, then add or subtract.• Area is in square units; don't confuse it with perimeter.

🧾 Quick revision sheet

Area of a parallelogram	base × perpendicular height
Area of a trapezium	½ × (a + b) × h, a and b parallel
Area of a circle	πr²
Area of a semicircle	½πr²
Units of area	Square units: cm², m².
Diameter 10 cm. Radius?	5 cm
Area of a circle of radius 7 cm (π = 22/7)	154 cm²