Geometry and Measures

What is the area of a rectangle with length 6 cm and width 4 cm?

• A48 cm²
• B10 cm²
• C24 cm²✓
• D20 cm²

Answer: Area of rectangle = length × width = 6 × 4 = 24 cm².

What is the perimeter of a square with side 5 cm?

• A15 cm
• B25 cm
• C20 cm✓
• D10 cm

Answer: Perimeter of square = 4 × side = 4 × 5 = 20 cm.

What is the volume of a cube with side 3 cm?

• A27 cm³✓
• B81 cm³
• C9 cm³
• D36 cm³

Answer: Volume of cube = side³ = 3³ = 27 cm³.

What is the area of a triangle with base 8 cm and height 5 cm?

• A13 cm²
• B80 cm²
• C40 cm²
• D20 cm²✓

Answer: Area of triangle = (base × height) ÷ 2 = (8 × 5) ÷ 2 = 20 cm².

How many millimetres are in 5 centimetres?

• A500 mm
• B5000 mm
• C50 mm✓
• D0.5 mm

Answer: 1 cm = 10 mm. So 5 cm = 5 × 10 = 50 mm.

How many metres are in 3.5 kilometres?

• A3.5 m
• B350 m
• C3500 m✓
• D35,000 m

Answer: 1 km = 1000 m. So 3.5 km = 3.5 × 1000 = 3500 m.

What is the volume of a cuboid with length 6 cm, width 4 cm, and height 3 cm?

• A144 cm³
• B72 cm³✓
• C13 cm³
• D36 cm³

Answer: Volume = length × width × height = 6 × 4 × 3 = 72 cm³.

What is the perimeter of a rectangle with length 10 cm and width 6 cm?

• A4 cm
• B32 cm✓
• C60 cm
• D16 cm

Answer: Perimeter = 2(length + width) = 2(10 + 6) = 2 × 16 = 32 cm.

How many grams are in 2.5 kilograms?

• A2500 g✓
• B0.25 g
• C25,000 g
• D250 g

Answer: 1 kg = 1000 g. So 2.5 kg = 2.5 × 1000 = 2500 g.

What is the area of a circle with radius 3 cm? (Use π ≈ 3.14)

• A9.42 cm²
• B18.84 cm²
• C28.26 cm²✓
• D113.04 cm²

Answer: Area = πr² = 3.14 × 3² = 3.14 × 9 = 28.26 cm².

What is the circumference of a circle with radius 5 cm? (Use π ≈ 3.14)

• A157 cm
• B78.5 cm
• C31.4 cm✓
• D15.7 cm

Answer: Circumference = 2πr = 2 × 3.14 × 5 = 31.4 cm.

What is the surface area of a cube with side 2 cm?

• A8 cm²
• B4 cm²
• C24 cm²✓
• D64 cm²

Answer: A cube has 6 faces. Area of each face = 2² = 4 cm². Total = 6 × 4 = 24 cm².

How many millilitres are in 2 litres?

• A200 ml
• B20 ml
• C2000 ml✓
• D20,000 ml

Answer: 1 litre = 1000 ml. So 2 litres = 2 × 1000 = 2000 ml.

A rectangle has area 48 cm² and length 8 cm. What is its width?

• A4 cm
• B8 cm
• C6 cm✓
• D12 cm

Answer: Width = Area ÷ length = 48 ÷ 8 = 6 cm.

What is the perimeter of a triangle with sides 5 cm, 6 cm, and 7 cm?

• A30 cm
• B12 cm
• C18 cm✓
• D11 cm

Answer: Perimeter = 5 + 6 + 7 = 18 cm.

How many metres are in 850 centimetres?

• A8.5 m✓
• B85,000 m
• C8500 m
• D85 m

Answer: 1 m = 100 cm. So 850 cm = 850 ÷ 100 = 8.5 m.

What is the area of a parallelogram with base 8 cm and height 6 cm?

• A48 cm²✓
• B96 cm²
• C28 cm²
• D24 cm²

Answer: Area of parallelogram = base × height = 8 × 6 = 48 cm².

A cuboid has volume 120 cm³, length 5 cm, and width 4 cm. What is its height?

• A10 cm
• B4 cm
• C6 cm✓
• D8 cm

Answer: Height = Volume ÷ (length × width) = 120 ÷ (5 × 4) = 120 ÷ 20 = 6 cm.

How many centimetres are in 0.4 metres?

• A4000 cm
• B4 cm
• C40 cm✓
• D400 cm

Answer: 1 m = 100 cm. So 0.4 m = 0.4 × 100 = 40 cm.

What is the diameter of a circle with radius 7 cm?

• A49 cm
• B7 cm
• C21 cm
• D14 cm✓

Answer: Diameter = 2 × radius = 2 × 7 = 14 cm.

Find the length of the hypotenuse in a right-angled triangle with sides 3 cm and 4 cm.

• A7 cm
• B√7 cm
• C5 cm✓
• D25 cm

Answer: Using Pythagoras' theorem: c² = a² + b² = 3² + 4² = 9 + 16 = 25. So c = 5 cm.

Find the length of the hypotenuse in a right-angled triangle with sides 5 cm and 12 cm.

• A17 cm
• B√17 cm
• C13 cm✓
• D√119 cm

Answer: c² = 5² + 12² = 25 + 144 = 169. So c = 13 cm.

In a right-angled triangle, the hypotenuse is 10 cm and one side is 6 cm. Find the other side.

• A8 cm✓
• B√136 cm
• C4 cm
• D√64 cm

Answer: Using c² = a² + b²: 10² = 6² + b². So 100 = 36 + b², giving b² = 64, so b = 8 cm.

In a right-angled triangle, the hypotenuse is 13 cm and one side is 5 cm. Find the other side.

• A12 cm✓
• B8 cm
• C10 cm
• D18 cm

Answer: 13² = 5² + b². So 169 = 25 + b², giving b² = 144, so b = 12 cm.

In a right-angled triangle, find sin(A) if the opposite side is 7 cm and the hypotenuse is 25 cm.

• A25/7
• B7/24
• C24/7
• D7/25✓

Answer: sin(A) = opposite/hypotenuse = 7/25.

In a right-angled triangle, find cos(A) if the adjacent side is 8 cm and the hypotenuse is 17 cm.

• A15/17
• B8/17✓
• C17/8
• D8/15

Answer: cos(A) = adjacent/hypotenuse = 8/17.

In a right-angled triangle, find tan(A) if the opposite side is 4 cm and the adjacent side is 3 cm.

• A4/3✓
• B4/5
• C3/4
• D3/5

Answer: tan(A) = opposite/adjacent = 4/3.

A reflection in the line y = x maps the point (2, 3) to which point?

• A(-2, -3)
• B(3, 2)✓
• C(-3, 2)
• D(3, -2)

Answer: A reflection in y = x swaps the x and y coordinates. So (2, 3) maps to (3, 2).

A reflection in the x-axis maps the point (4, 5) to which point?

• A(5, 4)
• B(-4, 5)
• C(-4, -5)
• D(4, -5)✓

Answer: A reflection in the x-axis negates the y-coordinate. So (4, 5) maps to (4, -5).

A rotation of 90° clockwise about the origin maps the point (2, 3) to which point?

• A(-3, 2)
• B(-2, -3)
• C(3, 2)
• D(3, -2)✓

Answer: A 90° clockwise rotation about the origin maps (x, y) to (y, -x). So (2, 3) maps to (3, -2).

A translation by the vector [3, -2] maps the point (1, 4) to which point?

• A(-2, 6)
• B(3, -2)
• C(4, 6)
• D(4, 2)✓

Answer: A translation by [3, -2] adds 3 to the x-coordinate and subtracts 2 from the y-coordinate. So (1, 4) maps to (1+3, 4-2) = (4, 2).

What is the length of the hypotenuse in a right-angled triangle with sides 6 cm and 8 cm?

• A10 cm✓
• B12 cm
• C20 cm
• D14 cm

Answer: c² = 6² + 8² = 36 + 64 = 100. So c = 10 cm.

Two triangles are congruent if they have the same shape and size. Which condition guarantees congruence?

• ASame perimeter
• BTwo angles equal
• CSSS (side-side-side)✓
• DSame area

Answer: SSS (all three sides equal) guarantees congruence. Same area or perimeter does not guarantee congruence.

Two triangles are similar if they have the same shape but not necessarily the same size. If triangle A has sides 3, 4, 5 and triangle B has sides 6, 8, 10, are they similar?

• ACannot determine
• BNo
• CYes✓
• DOnly if angles are equal

Answer: The sides of B are exactly twice those of A: 6/3 = 8/4 = 10/5 = 2. So they are similar with a scale factor of 2.

A trapezium has parallel sides of 8 cm and 12 cm, and a perpendicular height of 5 cm. What is its area?

• A25 cm²
• B100 cm²
• C480 cm²
• D50 cm²✓

Answer: Area of a trapezium = ½ x (a + b) x h = ½ x (8 + 12) x 5 = ½ x 20 x 5 = 50 cm². Leaving out the ½ gives 100 cm², and multiplying all three lengths gives 480 cm².

A cuboid measures 5 cm by 4 cm by 3 cm. What is its volume?

• A12 cm³
• B60 cm³✓
• C20 cm³
• D94 cm³

Answer: Volume of a cuboid = length x width x height = 5 x 4 x 3 = 60 cm³. Adding the three lengths gives 12, using only two of them gives 20, and 94 is the surface area in cm².

What is the volume of a cuboid with dimensions 2 cm, 3 cm, and 4 cm?

• A48 cm³
• B12 cm³
• C9 cm³
• D24 cm³✓

Answer: Volume = length × width × height = 2 × 3 × 4 = 24 cm³.

What is the surface area of a cube with side length 3 cm?

• A9 cm²
• B81 cm²
• C54 cm²✓
• D27 cm²

Answer: A cube has 6 faces, each with area 3² = 9 cm². Total surface area = 6 × 9 = 54 cm².

What is the volume of a cylinder with radius 2 cm and height 5 cm? (Use π ≈ 3.14)

• A10 cm³
• B62.8 cm³✓
• C125.6 cm³
• D20.3 cm³

Answer: Volume = πr²h = 3.14 × 2² × 5 = 3.14 × 4 × 5 = 62.8 cm³.

Two angles in a triangle are 45° and 60°. What is the third angle?

• A90°
• B45°
• C60°
• D75°✓

Answer: The sum of angles in a triangle is 180°. Third angle = 180 - 45 - 60 = 75°.