Area & Perimeter · Second Year
Area & Perimeter
Second Year · Rectangle, triangle & composite shapes · Tap NEXT to begin
Section 1 of 3
Rectangle & Square
Perimeter is the distance around the outside; area is the space inside.
The formulas
Area $A = \ell \times b$. Perimeter $P = 2\ell + 2b = 2(\ell + b)$.
Worked example — area and perimeter of a rectangle
A rectangle is $10$ m long and $6$ m wide. Find its area and perimeter.
$A = \ell \times b = 10 \times 6$
$P = 2(\ell + b) = 2(10 + 6)$
$A = 60\ \text{m}^2$, $P = 32\ \text{m}$
Section 2 of 3
Triangle
The formula
Area $= \dfrac{1}{2}\times \text{base}\times \text{perpendicular height}$. The height meets the base at $90^{\circ}$.
Now you try
You try
A triangle has base $12$ m and perpendicular height $7$ m. Find its area.
Pen and paper out — try it before you reveal.
$A = \tfrac{1}{2}bh = \tfrac{1}{2}(12)(7)$
$A = 42\ \text{m}^2$
$A = 42\ \text{m}^2$
Section 3 of 3
Composite Shapes
Split a compound shape into a rectangle and a triangle, find each area, then add.
You try
A house shape is a $15$ m by $3$ m rectangle with a triangular roof; the total height is $4.5$ m. Find the total area.
Pen and paper out — try it before you reveal.
Rectangle: $A = 15 \times 3 = 45\ \text{m}^2$
Roof triangle: base $15$, height $4.5 - 3 = 1.5$, so $A = \tfrac{1}{2}(15)(1.5) = 11.25\ \text{m}^2$
Total $= 45 + 11.25$
$56.25\ \text{m}^2$
$56.25\ \text{m}^2$
That’s Area & Perimeter.
Rectangle, triangle and composite shapes — split, find each area, and add.