Measurement
Mensuration
Find areas of trapeziums and circles, and volumes and surface areas of cuboids and cylinders.
Mensuration is measuring shapes: how much flat space a shape covers, and how much room a solid takes up. Area is measured in square units and volume in cubic units, and keeping those two apart is most of what goes wrong. If a formula multiplies two lengths together it is an area; three lengths together and it is a volume.
The formulas for this skill
Trapezium: half the sum of the parallel sides, times the height. Circle: area is π × r × r, circumference is 2 × π × r. Cuboid: volume is length × width × height, and its surface area is twice each of the three different faces added together. Cylinder: volume is the area of its circular base times its height, and its curved surface unrolls into a rectangle of circumference × height. Where a question says to take π = 22/7, use exactly that.
Worked example
Find the area of a circle with a radius of 21 cm, taking π = 22/7.
Write the formula with the numbers in: area = 22/7 × 21 × 21.
Getting the formula down before touching a calculator is what stops circumference and area being swapped.
Try it together
Now let us find the area of a trapezium together. Its parallel sides are 12 cm and 8 cm, and its height is 5 cm.
Add the parallel sides, halve, multiply by the height. The middle step is the one people skip.
1.Add the two parallel sides together. What do you get?
Have a go
Have a go on your own: a circle has a radius of 7 cm. Take π = 22/7. What is its area, in square centimetres?
Hint: Cancel the 7 into the 22/7 before you multiply anything.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.