BECE JHS
Area measures a surface. Volume measures the space inside a solid. The units are different, and the formulae must match the shape.
Area is in square units. A rectangle is length times breadth. A triangle is half times base times height, and the height must be perpendicular to the base. A parallelogram is base times perpendicular height. A trapezium is half times the sum of the parallel sides times the perpendicular distance between them. A circle is π times radius squared. When a question says take π as 22/7, use that value and do not leave an answer in terms of a different π.
Volume is in cubic units. A cuboid is length times breadth times height. A cube is the side cubed. For a prism, volume is the area of the constant cross section times the length. Do not mix the formulae. An area answer in cm³, or a volume answer in cm², loses the unit mark even when the number is right. Write the formula, substitute, then calculate.
The formula line is a mark, the substitution is a mark, and the answer with the correct unit is a mark. A correct number with the wrong unit does not get the unit mark. The height in a triangle or a trapezium is the perpendicular height, not a sloping side. If the question gives π as 22/7, a decimal from the calculator is not what the scheme wants.
These are practice questions in the style of the paper, with a model answer and a mark scheme. They are not a promise of what your paper will ask.
3 marks
A trapezium has parallel sides of 8 cm and 12 cm. The perpendicular distance between them is 5 cm. Find the area. (3 marks)
Area = 1/2 × (8 + 12) × 5 = 1/2 × 20 × 5 = 50 cm²
3 marks
A cuboid measures 5 cm by 4 cm by 3 cm.
(a) Find the volume. (2 marks)
(b) Find the area of the face that measures 5 cm by 4 cm. (1 mark)
(a) Volume = 5 × 4 × 3 = 60 cm³.
(b) Area = 5 × 4 = 20 cm².
2 marks
A triangle has a base of 10 cm and a perpendicular height of 6 cm. Find the area. (2 marks)
Area = 1/2 × 10 × 6 = 30 cm².
More questions on this topic are inside GLearn, marked as you answer, with the reason written out. The first ones need no account.
Practise Mathematics freeArea is the amount of surface, in square units such as cm². Volume is the space a solid takes up, in cubic units such as cm³. A rectangle has area. A cuboid has volume.
The perpendicular height, the line from the opposite corner that meets the base at a right angle. A sloping side is not the height unless the question shows that it is perpendicular to the base. All BECE Mathematics past questions