7.7 Shape and Measure

A rectangle has perimeter 24 cm. Give two different pairs of whole-number side lengths that would produce this perimeter. Verify each pair by adding.

A triangle has sides 6 cm, 8 cm and 11 cm. What is its perimeter? Show the addition.

A rectangle has area 36 cm² with whole-number sides. Give three different (length, width) pairs. Verify each by multiplying.

Find the area of a rectangle with length 7 cm and width 6 cm. Show the multiplication and write the units.

A right-angled triangle has base 10 cm and height 5 cm. Find its area. Explain why you halve the rectangle formula.

A shape has 4 sides and 2 lines of symmetry. Name two possibilities and justify each.

A cuboid has length 5 cm, width 4 cm and height 3 cm. Find its volume by multiplying length × width × height. Show each step.

A regular polygon has perimeter 48 cm and each side is 8 cm. Find the number of sides by dividing. State the name of the polygon.

A rectangle has perimeter 30 cm and length 11 cm. Find the width by calculation. Then find the area.

A compound shape is made from two rectangles. Rectangle A is 8 cm × 5 cm. Rectangle B is 4 cm × 3 cm. Find the total area by calculating each area separately then adding.

Find the area of a parallelogram with base 12 cm and perpendicular height 7 cm.

Find the area of a trapezium with parallel sides 6 cm and 10 cm and perpendicular height 5 cm.

Find the volume of a cuboid with length 8 cm, width 3 cm and height 4 cm.

Find the surface area of a cuboid with length 6 cm, width 4 cm and height 3 cm.

A compound shape is made from a rectangle 10 cm by 7 cm with a 3 cm square removed from one corner. Find the area.

Find the perimeter of a regular 7-sided polygon with side length 6 cm.

A net is folded to make a cuboid with dimensions 5 cm × 2 cm × 3 cm. How many faces does it have and what is its surface area?

A triangle has base 10 cm and area 35 cm². Find its perpendicular height.

How many faces, edges and vertices does a square-based pyramid have?

A rectangle has a perimeter of 40 cm and a length of 13 cm. Find its width and hence its area.

A rectangle has area 45 cm² and width 5 cm. Find its perimeter.

A square has side 2.5 cm. Find its area in cm² and then convert it to mm².

A trapezium has parallel sides 5 cm and 11 cm. Its area is 48 cm². Find its perpendicular height.

A compound L-shape is formed by a large rectangle 12 cm by 7 cm with a smaller rectangle 5 cm by 4 cm cut from one corner. Find the area of the L-shape.

A rectangle has length $(x + 5)$ cm and width $(3x)$ cm. Write an expression for its perimeter and simplify.

A rectangular garden is 4.5 m long and 1.8 m wide. Find its area in m² and convert the answer to cm².

A square has area 121 cm². Find its perimeter.

Find the surface area of a cuboid with dimensions 8 cm × 5 cm × 2 cm.

A rectangle is 15 cm long and 8 cm wide. What is 40% of its area?

A triangular prism has a triangular cross-section with base 8 cm and height 5 cm, and a length of 9 cm. Find its volume.

A rectangle has length $(2x + 3)$ cm and width $(x - 1)$ cm. Its perimeter is 40 cm. Find $x$ and hence find the area.

A compound shape is made by joining a rectangle 12 cm × 8 cm and a triangle with base 8 cm and height 5 cm along a shared edge of length 8 cm. Find the total area.

A cuboid fish tank is 1.5 m long, 0.6 m wide and 0.5 m deep. It is filled to 80% of its height. Find the volume of water in litres. (1 m³ = 1 000 litres.)

A square tile has perimeter 32 cm. Tiles are arranged in a 3 × 6 grid with no gaps. Find the total area of the tiled surface in cm² and convert to m².

Two identical trapeziums, each with parallel sides 7 cm and 13 cm and perpendicular height 8 cm, are placed together along their longer parallel side to form a parallelogram. Find the area of the parallelogram.

A rectangle has length 15 cm and width 6 cm. Both dimensions are increased by 10%. Find the new area and the percentage increase in area.

A cuboid has volume 210 cm³. Its length is 7 cm and its width is 5 cm. Find its height and hence its surface area.

The area of a square is 324 cm². Express 324 as a product of prime factors, and hence write down the exact side length of the square.

A path of uniform width 3 cm runs around the outside of a rectangle 14 cm × 8 cm. Find the area of the path alone.

A cube has surface area 486 cm². Find its side length, volume and express the volume in litres.