Year 6 Maths reasoning (SATs): Perimeter and area of rectangles, triangles, parallelograms and composite shapes
Part of the Year 6 Maths reasoning (SATs) measures in context chapter. Chapter overview · whole chapter on one page
Perimeter and area of rectangles, triangles, parallelograms and composite shapes
Rule
Rectangle: area = length x width. Triangle: area = base x perpendicular height / 2. Parallelogram: area = base x perpendicular height.
For a shape made of rectangles, find each area and add them. For perimeter, add all the outside sides.
Key ideas
- Use the perpendicular height for triangles and parallelograms.
- A triangle is half of a rectangle with the same base and height.
- The perimeter of a rectilinear shape is the total length of its outside edges.
Method. Multiply the length by the width.
- Write the formula. Area of a rectangle = length x width.12 x 7
- Multiply. Multiply the length by the width.12 x 7 = 84
- Write the units as square units. The area is measured in square cm.84 cm²
- Write the answer. 84 cm²
Check. 84 / 12 = 7. ✓
Watch out. Area is measured in square units, so the answer ends with a small 2, such as cm².
Method. Multiply the base by the height, then halve.
- Write the formula. Area of a triangle = base x height / 2.10 x 6 / 2
- Multiply the base and the height. Multiply first.10 x 6 = 60
- Halve the answer. A triangle is half of a rectangle with the same base and height.60 / 2 = 30
- Write the answer. Square units for area.30 cm²
- Write the answer. 30 cm²
Check. A rectangle 10 by 6 has area 60, and half of it is 30. ✓
Watch out. Use the perpendicular height, not the slanted side.
Method. Split the shape into rectangles, find each area, then add.
- Split the shape into two rectangles. Rectangle 1 is 6 cm by 4 cm; rectangle 2 is 3 cm by 2 cm.6 x 4 and 3 x 2
- Find each area. Multiply the length and width of each rectangle.24 and 6
- Add the areas. The total area is the sum of the two parts.24 + 6 = 30
- Write the answer. Square units for area.30 cm²
- Write the answer. 30 cm²
Check. 24 + 6 = 30. ✓
Watch out. Check that the two rectangles do not overlap.
Watch out
Watch out. Do not use the slanted side of a triangle or a parallelogram. Use the perpendicular height.
Exam tip
Practice guide. Draw the shape and label the lengths before you multiply.
Exercise 4D Practice: perimeter and area
Non-calculatorMethod. Multiply the length by the width.
- Write the formula. Area of a rectangle = length x width.15 x 8
- Multiply. Multiply the length by the width.15 x 8 = 120
- Write the units as square units. The area is measured in square m.120 m²
- Write the answer. 120 m²
Check. 120 / 15 = 8. ✓
Watch out. Area is measured in square units, so the answer ends with a small 2, such as cm².
Method. Multiply the base by the height, then halve.
- Write the formula. Area of a triangle = base x height / 2.7 x 4 / 2
- Multiply the base and the height. Multiply first.7 x 4 = 28
- Halve the answer. A triangle is half of a rectangle with the same base and height.28 / 2 = 14
- Write the answer. Square units for area.14 cm²
- Write the answer. 14 cm²
Check. A rectangle 7 by 4 has area 28, and half of it is 14. ✓
Watch out. Use the perpendicular height, not the slanted side.
Method. Multiply the base by the height, then halve.
- Write the formula. Area of a triangle = base x height / 2.9 x 6 / 2
- Multiply the base and the height. Multiply first.9 x 6 = 54
- Halve the answer. A triangle is half of a rectangle with the same base and height.54 / 2 = 27
- Write the answer. Square units for area.27 cm²
- Write the answer. 27 cm²
Check. A rectangle 9 by 6 has area 54, and half of it is 27. ✓
Watch out. Use the perpendicular height, not the slanted side.
Method. Multiply the base by the perpendicular height. No halving is needed.
- Write the formula. Area of a parallelogram = base x perpendicular height.11 x 5
- Multiply. Multiply the base by the perpendicular height.11 x 5 = 55
- Write the answer. Square units for area.55 cm²
- Write the answer. 55 cm²
Check. A rectangle 11 by 5 has the same area. ✓
Watch out. A parallelogram is not halved, unlike a triangle with the same base and height.
Method. Split the shape into rectangles, find each area, then add.
- Split the shape into two rectangles. Rectangle 1 is 8 m by 5 m; rectangle 2 is 4 m by 3 m.8 x 5 and 4 x 3
- Find each area. Multiply the length and width of each rectangle.40 and 12
- Add the areas. The total area is the sum of the two parts.40 + 12 = 52
- Write the answer. Square units for area.52 m²
- Write the answer. 52 m²
Check. 40 + 12 = 52. ✓
Watch out. Check that the two rectangles do not overlap.
Method. Split the shape into rectangles, find each area, then add.
- Split the shape into two rectangles. Rectangle 1 is 10 cm by 3 cm; rectangle 2 is 4 cm by 6 cm.10 x 3 and 4 x 6
- Find each area. Multiply the length and width of each rectangle.30 and 24
- Add the areas. The total area is the sum of the two parts.30 + 24 = 54
- Write the answer. Square units for area.54 cm²
- Write the answer. 54 cm²
Check. 30 + 24 = 54. ✓
Watch out. Check that the two rectangles do not overlap.
Method. Add all four sides, or use 2 x (length + width).
- Add the four sides. 9 + 4 + 9 + 4 = 26.26
- Check. 2 x (9 + 4) = 2 x 13 = 26.26
- Write the answer. 26
Check. 26 / 2 = 13 = 9 + 4. ✓
Method. A cut-out corner does not change the outside perimeter, so use the big rectangle.
- Outside sides. The notch moves inwards, but the outside edges still add to the whole rectangle.10 + 6 + 10 + 6
- Add. 10 + 6 + 10 + 6 = 32 m.32 m
- Write the answer. 32
Check. 2 x (10 + 6) = 32. ✓
Watch out. A notch cut from a corner does not change the perimeter, so the big rectangle gives the answer.
Method. Find the area of the whole poster with the border, then take away the poster.
- Outside size. With 5 cm on each side the length is 40 + 10 = 50 cm, and the width is 30 + 10 = 40 cm.50 x 40
- Area with border. 50 x 40 = 2000 square cm.2000
- Area of the border. 2000 - (40 x 30) = 2000 - 1200 = 800 square cm.800
- Write the answer. 800
Check. 1200 + 800 = 2000. ✓
Method. Use base x height / 2.
- Multiply. 8 x 5 = 40.40
- Halve. 40 / 2 = 20 square cm.20 square cm
- Write the answer. 20 square cm
Check. Sam forgot to halve. ✓
Method. Test each choice against the question.
- Read what the question asks. Decide what the answer must do or show.
- Test the choice. A parallelogram is the same as a rectangle with the same base and height, so its area is base x height. A triangle is half of that.the parallelogram fits
- Reject the other choices. The triangle has half the area, so the others are wrong.the triangle and they are the same do not fit
- Write the answer. the parallelogram
Check. the parallelogram is the one that fits. ✓
Method. Use area = base x height / 2, and work backwards.
- Double the area. 30 x 2 = 60.60
- Divide by the base. 60 / 10 = 6 cm.6 cm
- Write the answer. 6
Check. 10 x 6 / 2 = 30. ✓
Method. Compare the perpendicular height with the slanted side.
- Identify the height. The perpendicular height goes straight across, at right angles to the base.perpendicular
- Compare. The slanted side is longer than the height, so 5 cm is a sensible height.5 cm < 9 cm
- Write the answer. Because the perpendicular height is the straight-up distance, which can be shorter than the slanted side.
Check. The perpendicular is shorter than the slanted side. ✓
Method. Split the shape into rectangles, find each area, then add.
- Split the shape into two rectangles. Rectangle 1 is 12 cm by 2 cm; rectangle 2 is 5 cm by 3 cm.12 x 2 and 5 x 3
- Find each area. Multiply the length and width of each rectangle.24 and 15
- Add the areas. The total area is the sum of the two parts.24 + 15 = 39
- Write the answer. Square units for area.39 cm²
- Write the answer. 39 cm²
Check. 24 + 15 = 39. ✓
Watch out. Check that the two rectangles do not overlap.
Method. Find the area of the rectangle, then take away the triangle.
- Rectangle. 14 x 6 = 84 square cm.84
- Triangle. 6 x 4 / 2 = 12 square cm.12
- Left. 84 - 12 = 72 square cm.72
- Write the answer. 72
Check. 72 + 12 = 84. ✓