Geometry & Measures

What is the area of a rectangle 8 cm long and 5 cm wide?

• A26 cm²
• B40 cm²✓
• C80 cm²
• D13 cm²

Answer: Area of a rectangle = length × width = 8 × 5 = 40 cm².

What is the sum of the interior angles of a triangle?

• A90°
• B180°✓
• C360°
• D270°

Answer: The interior angles of any triangle always add up to 180°.

What is the perimeter of a square with side length 7 cm?

• A28 cm✓
• B14 cm
• C49 cm
• D21 cm

Answer: Perimeter = 4 × side = 4 × 7 = 28 cm.

A circle has radius 5 cm. What is its diameter?

• A5 cm
• B2.5 cm
• C10 cm✓
• D25 cm

Answer: Diameter = 2 × radius = 2 × 5 = 10 cm.

Angles on a straight line add up to:

• A180°✓
• B360°
• C90°
• D270°

Answer: Angles on a straight line are supplementary and sum to 180°.

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

• A9 cm³
• B12 cm³
• C27 cm³✓
• D18 cm³

Answer: Volume of a cube = side³ = 3 × 3 × 3 = 27 cm³.

How many degrees are there in a full turn?

• A90°
• B720°
• C180°
• D360°✓

Answer: A full turn (complete rotation) is 360°.

A right angle measures:

• A180°
• B360°
• C45°
• D90°✓

Answer: A right angle is exactly 90°.

A right-angled triangle has shorter sides of 6 cm and 8 cm. How long is the hypotenuse?

• A14 cm
• B100 cm
• C10 cm✓
• D48 cm

Answer: Squaring the two shorter sides gives 36 + 64 = 100, and the hypotenuse is the square root of that, so it is 10 cm. Adding 6 and 8 gives 14 cm and forgets the squaring altogether.

A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 5 cm. How long is the other shorter side?

• A14 cm
• B8 cm
• C12 cm✓
• D18 cm

Answer: To find a shorter side you subtract the squares: 13² - 5² = 169 - 25 = 144, and the square root of 144 is 12 cm. Subtracting the lengths themselves gives 8 cm, which skips the squaring.

A circle has a diameter of 14 cm. Taking π as 3.14, what is its circumference to 1 decimal place?

• A87.9 cm
• B153.9 cm
• C22.0 cm
• D44.0 cm✓

Answer: Circumference is π × diameter, so 3.14 × 14 = 43.96, which is 44.0 cm to 1 decimal place. Treating 14 cm as the radius doubles the answer to 87.9 cm.

A circle has a radius of 5 cm. Taking π as 3.14, what is its area?

• A31.4 cm²
• B15.7 cm²
• C314 cm²
• D78.5 cm²✓

Answer: Area is π × radius², so 3.14 × 5² = 3.14 × 25 = 78.5 cm². Working out 2 × 3.14 × 5 instead gives 31.4, which is the circumference in cm.

A trapezium has parallel sides of 6 cm and 10 cm and a perpendicular height of 4 cm. What is its area?

• A32 cm²✓
• B64 cm²
• C240 cm²
• D20 cm²

Answer: Add the parallel sides, halve the total, then multiply by the height: (6 + 10) ÷ 2 = 8, and 8 × 4 = 32 cm². Missing out the halving step gives 64 cm².

A parallelogram has a base of 9 cm, a perpendicular height of 5 cm and a slanted side of 6 cm. What is its area?

• A54 cm²
• B22.5 cm²
• C30 cm²
• D45 cm²✓

Answer: The area of a parallelogram is base × perpendicular height, so 9 × 5 = 45 cm². The 6 cm slanted side is not the perpendicular height, and halving the answer applies only to a triangle.

A triangular prism has a cross-section of area 12 cm² and a length of 7 cm. What is its volume?

• A19 cm³
• B42 cm³
• C84 cm³✓
• D168 cm³

Answer: The volume of any prism is the area of the cross-section multiplied by the length: 12 × 7 = 84 cm³. Halving again is wrong because the triangle shape is already accounted for in the 12 cm².

A cuboid measures 5 cm by 3 cm by 2 cm. What is its total surface area?

• A30 cm²
• B62 cm²✓
• C31 cm²
• D124 cm²

Answer: The three different faces have areas 5 × 3 = 15, 5 × 2 = 10 and 3 × 2 = 6 cm², and each of those appears twice, so the total is 2 × 31 = 62 cm². The figure 30 is the volume in cm³, not an area.

Two parallel lines are crossed by a transversal. One angle between the parallel lines measures 65°. What is the size of the co-interior (allied) angle on the same side of the transversal?

• A65°
• B115°✓
• C130°
• D25°

Answer: Co-interior angles lie between the parallel lines on the same side of the transversal and always add up to 180°, so the other angle is 180 - 65 = 115°. Alternate and corresponding angles are the pairs that are equal.

What is the size of each exterior angle of a regular hexagon?

• A60°✓
• B120°
• C720°
• D45°

Answer: The exterior angles of any polygon add up to 360°, so each one in a regular hexagon is 360 ÷ 6 = 60°. The angle of 120° is the interior angle, and 720° is the sum of all six interior angles.

The point (3, 1) is reflected in the y-axis. What are the coordinates of the image?

• A(3, -1)
• B(-3, 1)✓
• C(-3, -1)
• D(1, 3)

Answer: Reflecting in the y-axis keeps the y-coordinate the same and reverses the sign of the x-coordinate, giving (-3, 1). Reflecting in the x-axis is what would produce (3, -1).

A shape is rotated 90° clockwise and then translated 3 units to the right. How does the final image compare with the original shape?

• AIt is congruent to the original✓
• BIt is an enlargement
• CIt is similar, not congruent
• DIts angles are each 90° larger

Answer: Rotations and translations move a shape without changing any of its lengths or angles, so the image is congruent to the original. Only an enlargement changes the lengths and leaves a shape that is similar but not congruent.

A rectangle is enlarged by a scale factor of 3. What happens to its angles and its side lengths?

• AThe angles triple but the sides do not
• BThe angles and the sides both triple
• CThe angles stay the same and the sides triple✓
• DThe angles and the sides both stay the same

Answer: An enlargement multiplies every length by the scale factor but leaves every angle unchanged, which is why the enlarged shape is similar to the original. Angles are never multiplied by a scale factor.