Geometry and Measures: Angles, Area and Volume

Angles, area and volume

Geometry is the maths of shape and space, and it turns up everywhere, from tiling a floor to filling a tank. This module covers three big ideas. First, angles: the rules that tell you how the angles in lines, triangles and other shapes fit together, so you can find a missing one without measuring. Second, area and perimeter: how much flat space a shape covers, and how far it is around the edge. Third, volume: how much space a solid holds. You will also see why the units matter, since a length, an area and a volume are each measured in a different kind of unit. Get the rule and the unit right, and geometry becomes a set of reliable tools rather than guesswork.

Words for geometry and measures

Learn these terms before the area rules are matched up. They name the ideas used in geometry and measures.

Match each shape to its area rule

Perimeter against area

Two questions people mix up are how far it is around a shape and how much space it covers. They are different, and they use different units.

How many degrees in a triangle?

The three angles inside any triangle always add up to the same total. What is it?

• One hundred and eighty degrees
• Ninety degrees
• Three hundred and sixty degrees
• Two hundred and seventy degrees

Angle rules on parallel lines

When a straight line crosses a pair of parallel lines, it creates matching angles. Alternate angles, which sit on opposite sides of the crossing line, are equal. Corresponding angles, which sit in the same position at each crossing, are also equal. Spotting these lets you find a missing angle without measuring. Look for the shapes the lines make: alternate angles form a letter Z, and corresponding angles form a letter F. Once you can name the rule you are using, you can explain your answer, which is what earns full marks. Always state which rule you used, not just the number.

Pick the true angle facts

Select every statement about angles that is true.

• Angles on a straight line add up to one hundred and eighty degrees
• Angles around a point add up to three hundred and sixty degrees
• The angles in a triangle add up to one hundred and eighty degrees
• Every angle is ninety degrees
• Angles never add up to anything

Order how to find a volume

Put the steps of finding the volume of a box-shaped solid into a sensible order.

• Read off the length, width and height
• Check they are all in the same units
• Multiply length by width by height
• Give the answer in cubic units
• Check the answer looks sensible

Complete the geometry facts

The distance all the way around a shape is its _____. The amount of flat space inside a shape is its _____. The amount of space inside a solid is its _____. The angles inside any triangle add up to one hundred and eighty _____.

Tap the two correct area statements

Read these four statements about area. Tap the TWO that are correct.

• the area of a rectangle is length times width
• the area of a triangle is half of base times height
• the area of a rectangle is length plus width
• the area of a circle is two times the radius

A fence, some turf and a pond

Think of a garden to picture these three measures. The fence you put around the edge is like the distance around a shape. The turf you lay to cover the ground is like the flat space inside it. And if you built a pond and filled it with water, the water needed is like the space inside a solid. Same garden, three different questions: how far around, how much to cover, how much to fill. Knowing which question is being asked is half the battle, because each one is worked out in a different way and measured in a different kind of unit.

Work out the area of the rectangle

A rectangle is eight centimetres long and five centimetres wide. What is its area in square centimetres? Give the number only.

Choose the right measure

Read each situation and choose the best answer.

• You want to put a fence right around a rectangular garden. What do you need to work out?
• You want to buy turf to cover a flat lawn. What do you need?
• You want to know how much water fills a tank. What do you need?

Build a geometry rule

Choose the word for each gap to complete one rule about shape and space.

Explain angles, area and volume

A friend finds geometry confusing and mixes up perimeter, area and volume. Using what you have learned, explain the main ideas clearly.

• Explain what an angle is and one angle rule you know
• Explain the difference between perimeter and area
• Explain how to find the area of a rectangle and a triangle
• Explain what volume measures and how to find it for a box shape
• Explain why using the right units matters