Level 3 · Ages 11–13
Read it again any time, including while you work through the exercises.
You know how to find the area of a rectangle: length × width. Good news, this formula will unlock cooler shapes: the triangle and the disc!
Let us start with the triangle. Draw a rectangle, then draw a diagonal: you get two triangles that match exactly. So each triangle is half of the rectangle. That is where the formula comes from: area of a triangle = (base × height) ÷ 2.
The base is one side of the triangle. The height is the perpendicular distance between that side and the opposite vertex. Careful: the height is not always a side of the triangle! On a slanted triangle, it drops straight down like a plumb line.
For the disc (the inside of a circle), the formula uses the famous number pi, written π, which is about 3.14. Area of a disc = π × radius × radius, written π × r². The radius is the distance from the centre to the edge.
Ultra classic trap: you are often given the diameter (all the way across the disc) instead of the radius. The radius is half the diameter. Always check what you are given before rushing into the formula!
Compute the area of a triangle with base 8 cm and height 5 cm.
A = (b × h) ÷ 2
A triangle is half a rectangle with the same base and height: I multiply then divide by 2.
8 × 5 = 40
First I compute the full rectangle: 8 × 5 = 40.
40 ÷ 2 = 20
Then I take half: 40 ÷ 2 = 20.
Result: The triangle's area is 20 cm².
Compute the area of a disc with radius 10 cm (take π ≈ 3.14).
A = π × r²
The disc formula: pi times the radius squared.
r² = 10 × 10 = 100
I start with the square of the radius: 10 × 10 = 100.
3,14 × 100 = 314
Then I multiply by π ≈ 3.14: that gives 314.
Result: The disc's area is about 314 cm².