Year 5: Rectangles: sides and angles
Part of the Year 5 angles and shapes chapter. Chapter overview · whole chapter on one page
Rectangles: sides and angles
A rectangle has four right angles. Its opposite sides are equal in length. Four right angles make a whole turn, because 4 × 90° = 360°. We can use these facts to find missing lengths and angles.
Key ideas
- Opposite sides of a rectangle are equal.
- Every corner of a rectangle is a right angle, which is 90°.
- Use a known side to find a missing side. Use 90° and 360° to find missing angles.
Key words. A rectangle has four right angles. Its opposite sides are equal in length. The perimeter is the distance all the way round the outside.
Method. Opposite sides of a rectangle are always the same length.
- Find the side opposite the top side. Opposite sides of a rectangle are equal.the opposite side is 8.5 cm
- Check the other pair of sides. Both pairs of opposite sides must match.the other pair also matches
- Write the answer. 8.5 cm
Check. Both sides are 8.5 cm. ✓
Watch out. Opposite sides match. Sides next to each other do not have to match.
Method. Add the known parts of the long side, then take them away from 12.
- Add the parts we know. The parts of the long side that we know are 5.5
- Take this away from 12. The parts of the long side add up to 12, so the missing one is what is left.12 − 5 = 7
- Write the answer. 7 cm
Check. 5 + 7 = 12. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
Method. Add the known angles at the corner, then take them away from 90.
- Add the parts we know. The angles at the corner that we know are 35.35
- Take this away from 90. The angles at the corner add up to 90, so the missing one is what is left.90 − 35 = 55
- Write the answer. 55°
Check. 35 + 55 = 90. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
Watch out
A common mistake is to think that the sides next to each other are equal. Only opposite sides are equal. Also, a right angle is 90°, not 100°.
Exercise 9E Rectangles: missing lengths and angles
Non-calculatorKey words. A rectangle has four right angles. Its opposite sides are equal in length. The perimeter is the distance all the way round the outside.
Method. Opposite sides of a rectangle are always the same length.
- Find the side opposite the bottom side. Opposite sides of a rectangle are equal.the opposite side is 10 cm
- Check the other pair of sides. Both pairs of opposite sides must match.the other pair also matches
- Write the answer. 10 cm
Check. Both sides are 10 cm. ✓
Watch out. Opposite sides match. Sides next to each other do not have to match.
Key words. A rectangle has four right angles. Its opposite sides are equal in length. The perimeter is the distance all the way round the outside.
Method. Opposite sides of a rectangle are always the same length.
- Find the side opposite the left side. Opposite sides of a rectangle are equal.the opposite side is 4 cm
- Check the other pair of sides. Both pairs of opposite sides must match.the other pair also matches
- Write the answer. 4 cm
Check. Both sides are 4 cm. ✓
Watch out. Opposite sides match. Sides next to each other do not have to match.
Key words. A rectangle has four right angles. Its opposite sides are equal in length. The perimeter is the distance all the way round the outside.
Method. The perimeter is the distance all the way round, so add all four sides.
- Add the two long sides. A rectangle has two long sides of the same length.15 + 15 = 30
- Add the two short sides. It also has two short sides of the same length.6 + 6 = 12
- Add all four sides. The perimeter is the total of all the sides.30 + 12 = 42
- Write the answer. 42 cm
Check. 2 × (15 + 6) = 42. ✓
Watch out. Do not forget the second long side and the second short side.
Key words. A rectangle has four right angles. Its opposite sides are equal in length. The perimeter is the distance all the way round the outside.
Method. Half of the perimeter is one length and one width. Find the missing side from that.
- Halve the perimeter. Half of the perimeter is one long side and one short side added together.30 ÷ 2 = 15
- Take away the side we know. What is left is the other side.15 − 9 = 6
- Write the answer. 6 cm
Check. 2 × (6 + 9) = 30. ✓
Watch out. Halve the perimeter first. Do not take the known side away from the whole perimeter.
Key words. A rectangle has four right angles. Its opposite sides are equal in length. The perimeter is the distance all the way round the outside.
Method. Half of the perimeter is one length and one width. Find the missing side from that.
- Halve the perimeter. Half of the perimeter is one long side and one short side added together.24 ÷ 2 = 12
- Take away the side we know. What is left is the other side.12 − 5 = 7
- Write the answer. 7 cm
Check. 2 × (7 + 5) = 24. ✓
Watch out. Halve the perimeter first. Do not take the known side away from the whole perimeter.
Method. Add the known parts of the long side, then take them away from 15.
- Add the parts we know. The parts of the long side that we know are 6.6
- Take this away from 15. The parts of the long side add up to 15, so the missing one is what is left.15 − 6 = 9
- Write the answer. 9 cm
Check. 6 + 9 = 15. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
Method. Add the known angles at the corner, then take them away from 90.
- Add the parts we know. The angles at the corner that we know are 62.62
- Take this away from 90. The angles at the corner add up to 90, so the missing one is what is left.90 − 62 = 28
- Write the answer. 28°
Check. 62 + 28 = 90. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
Method. Add the known angles at the corner, then take them away from 90.
- Add the parts we know. The angles at the corner that we know are 48.48
- Take this away from 90. The angles at the corner add up to 90, so the missing one is what is left.90 − 48 = 42
- Write the answer. 42°
Check. 48 + 42 = 90. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
Key words. An angle is the amount of turn between two lines (the arms) that meet at a point (the vertex). We measure angles in degrees, written with the symbol °.
Method. Learn these facts about turns: a right angle is 90, a half turn is 180 and a whole turn is 360.
- Recall the fact. Every corner of a rectangle is a right angle.one corner of a rectangle = 90°
- Write the answer. 90°
Check. 90 is the right number for one corner of a rectangle. ✓
Watch out. A whole turn is bigger than a half turn, and a half turn is bigger than a right angle.
Key words. A rectangle has four right angles. Its opposite sides are equal in length. The perimeter is the distance all the way round the outside.
Method. Count the corners, then multiply by the size of one corner.
- Count the corners. A rectangle has 4 corners.4 corners
- Multiply by 90°. Each corner is a right angle.4 × 90 = 360
- Write the answer. 360°
Check. 360 ÷ 4 = 90. ✓
Watch out. Four right angles make a whole turn.
Key words. A rectangle has four right angles. Its opposite sides are equal in length. The perimeter is the distance all the way round the outside.
Method. Half of the perimeter is one length and one width. Find the missing side from that.
- Halve the perimeter. Half of the perimeter is one long side and one short side added together.20 ÷ 2 = 10
- Take away the side we know. What is left is the other side.10 − 6 = 4
- Write the answer. 4 cm
Check. 2 × (4 + 6) = 20. ✓
Watch out. Halve the perimeter first. Do not take the known side away from the whole perimeter.
Key words. A rectangle has four right angles. Its opposite sides are equal in length. The perimeter is the distance all the way round the outside.
Method. Find the length first, then add all four sides.
- Find the length. The length is 4 cm more than the width.3 + 4 = 7 cm
- Add the four sides. Two sides are 7 cm and two sides are 3 cm.7 + 3 + 7 + 3 = 20 cm
- Write the answer. 20 cm
Check. 2 × (7 + 3) = 20. ✓
Watch out. Find the length before you add the sides.
Key words. A rectangle has four right angles. Its opposite sides are equal in length. The perimeter is the distance all the way round the outside.
Method. Think about the rules for the sides of a rectangle.
- Think about a square. A square has four equal sides and four right angles, so it is a rectangle.square = rectangle
- Push the shape over. The sides stay equal when the shape leans, but the corners are no longer right angles.equal sides, not right angles
- Decide. So a shape with four equal sides is not always a rectangle.No
Check. A rectangle needs four right angles as well as opposite sides that are equal. ✓
Watch out. Four equal sides are not enough. A rectangle also needs four right angles.
Key words. A rectangle has four right angles. Its opposite sides are equal in length. The perimeter is the distance all the way round the outside.
Method. Look at the pairs of opposite sides.
- Look at the pairs of opposite sides. A rectangle has two pairs of equal opposite sides.pairs: 5 and 5, 6 and 7
- Compare the second pair. The two sides of this pair must be equal.6 ≠ 7
- Decide. So this shape cannot be a rectangle.No
Check. The other pair, 5 cm and 5 cm, is equal, but 6 cm and 7 cm are not. ✓
Watch out. Check both pairs of opposite sides, not just one.