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Home / Practice / Maths
Rectangles, triangles and L-shapes, and knowing which one the question wants.
Question 1 of 12
A rectangle has an area of 240 cm² and one side is 15 cm. How long is the other side?
Area is length × width, so finding a missing side means dividing rather than multiplying: 240 ÷ 15 = 16. The other side is 16 cm. Subtracting gives 225, which comes from treating the area as though it were a perimeter. Checking forwards: 15 × 16 = 240, which is the area given. Watch the units: cm² is an area, cm is a length. The answer here is a length.
The answer is C. Area is length × width, so finding a missing side means dividing rather than multiplying: 240 ÷ 15 = 16. The other side is 16 cm. Subtracting gives 225, which comes from treating the area as though it were a perimeter. Checking forwards: 15 × 16 = 240, which is the area given. Watch the units: cm² is an area, cm is a length. The answer here is a length.
A rectangle is 3 cm long and 5 cm wide. What is its area?
Area is the space inside, found by multiplying the two sides: 3 × 5 = 15. The units are cm², because two lengths have been multiplied together. The perimeter would be 16 cm, which is the distance all the way round — a different question.
The answer is B. Area is the space inside, found by multiplying the two sides: 3 × 5 = 15. The units are cm², because two lengths have been multiplied together. The perimeter would be 16 cm, which is the distance all the way round — a different question.
A rectangle has an area of 150 cm² and one side is 10 cm. How long is the other side?
Area is length × width, so finding a missing side means dividing rather than multiplying: 150 ÷ 10 = 15. The other side is 15 cm. Subtracting gives 140, which comes from treating the area as though it were a perimeter. Checking forwards: 10 × 15 = 150, which is the area given. Watch the units: cm² is an area, cm is a length. The answer here is a length.
The answer is C. Area is length × width, so finding a missing side means dividing rather than multiplying: 150 ÷ 10 = 15. The other side is 15 cm. Subtracting gives 140, which comes from treating the area as though it were a perimeter. Checking forwards: 10 × 15 = 150, which is the area given. Watch the units: cm² is an area, cm is a length. The answer here is a length.
An L-shaped room is made from two rectangles. The larger is 6 m by 9 m. The smaller, joined along one edge, is 4 m by 7 m. What is the total area of the floor?
Split the shape into the two rectangles and work them out separately. The larger is 6 × 9 = 54 m². The smaller is 4 × 7 = 28 m². Adding them gives 54 + 28 = 82 m². Multiplying the overall length by the overall width would count the corner that is not there, giving 160 m² — far too large. Cut a compound shape into rectangles first, then add. Never try to do it in one multiplication.
The answer is A. Split the shape into the two rectangles and work them out separately. The larger is 6 × 9 = 54 m². The smaller is 4 × 7 = 28 m². Adding them gives 54 + 28 = 82 m². Multiplying the overall length by the overall width would count the corner that is not there, giving 160 m² — far too large. Cut a compound shape into rectangles first, then add. Never try to do it in one multiplication.
A triangle has a base of 4 cm and a perpendicular height of 6 cm. What is its area?
A triangle is exactly half of the rectangle that would fit round it. That rectangle would have area 4 × 6 = 24 cm², so the triangle is 24 ÷ 2 = 12 cm². Forgetting to halve is the mistake this question exists to catch. "Perpendicular height" means straight up from the base, not the sloping side. The height must be at right angles to the base. A sloping side is longer and gives a wrong answer.
The answer is B. A triangle is exactly half of the rectangle that would fit round it. That rectangle would have area 4 × 6 = 24 cm², so the triangle is 24 ÷ 2 = 12 cm². Forgetting to halve is the mistake this question exists to catch. "Perpendicular height" means straight up from the base, not the sloping side. The height must be at right angles to the base. A sloping side is longer and gives a wrong answer.
A rectangle is 9 cm long and 4 cm wide. What is its perimeter?
Perimeter is the distance all the way round, so every side counts. A rectangle has two sides of 9 cm and two of 4 cm: 9 + 4 + 9 + 4 = 26 cm. Adding 9 + 4 = 13 gives only half of it, which is the usual slip. The area would be 36 cm², which is a different question.
The answer is B. Perimeter is the distance all the way round, so every side counts. A rectangle has two sides of 9 cm and two of 4 cm: 9 + 4 + 9 + 4 = 26 cm. Adding 9 + 4 = 13 gives only half of it, which is the usual slip. The area would be 36 cm², which is a different question.
An L-shaped room is made from two rectangles. The larger is 6 m by 12 m. The smaller, joined along one edge, is 3 m by 6 m. What is the total area of the floor?
Split the shape into the two rectangles and work them out separately. The larger is 6 × 12 = 72 m². The smaller is 3 × 6 = 18 m². Adding them gives 72 + 18 = 90 m². Multiplying the overall length by the overall width would count the corner that is not there, giving 162 m² — far too large. Cut a compound shape into rectangles first, then add. Never try to do it in one multiplication.
The answer is B. Split the shape into the two rectangles and work them out separately. The larger is 6 × 12 = 72 m². The smaller is 3 × 6 = 18 m². Adding them gives 72 + 18 = 90 m². Multiplying the overall length by the overall width would count the corner that is not there, giving 162 m² — far too large. Cut a compound shape into rectangles first, then add. Never try to do it in one multiplication.
An L-shaped room is made from two rectangles. The larger is 12 m by 12 m. The smaller, joined along one edge, is 8 m by 8 m. What is the total area of the floor?
Split the shape into the two rectangles and work them out separately. The larger is 12 × 12 = 144 m². The smaller is 8 × 8 = 64 m². Adding them gives 144 + 64 = 208 m². Multiplying the overall length by the overall width would count the corner that is not there, giving 400 m² — far too large. Check the answer is bigger than the larger rectangle alone but smaller than the whole enclosing rectangle.
The answer is B. Split the shape into the two rectangles and work them out separately. The larger is 12 × 12 = 144 m². The smaller is 8 × 8 = 64 m². Adding them gives 144 + 64 = 208 m². Multiplying the overall length by the overall width would count the corner that is not there, giving 400 m² — far too large. Check the answer is bigger than the larger rectangle alone but smaller than the whole enclosing rectangle.
A triangle has a base of 8 cm and a perpendicular height of 5 cm. What is its area?
A triangle is exactly half of the rectangle that would fit round it. That rectangle would have area 8 × 5 = 40 cm², so the triangle is 40 ÷ 2 = 20 cm². Forgetting to halve is the mistake this question exists to catch. "Perpendicular height" means straight up from the base, not the sloping side. The height must be at right angles to the base. A sloping side is longer and gives a wrong answer.
The answer is D. A triangle is exactly half of the rectangle that would fit round it. That rectangle would have area 8 × 5 = 40 cm², so the triangle is 40 ÷ 2 = 20 cm². Forgetting to halve is the mistake this question exists to catch. "Perpendicular height" means straight up from the base, not the sloping side. The height must be at right angles to the base. A sloping side is longer and gives a wrong answer.
A rectangle is 12 cm long and 3 cm wide. What is its area?
Area is the space inside, found by multiplying the two sides: 12 × 3 = 36. The units are cm², because two lengths have been multiplied together. The perimeter would be 30 cm, which is the distance all the way round — a different question.
The answer is D. Area is the space inside, found by multiplying the two sides: 12 × 3 = 36. The units are cm², because two lengths have been multiplied together. The perimeter would be 30 cm, which is the distance all the way round — a different question.
A rectangle has an area of 144 cm² and one side is 12 cm. How long is the other side?
Area is length × width, so finding a missing side means dividing rather than multiplying: 144 ÷ 12 = 12. The other side is 12 cm. Subtracting gives 132, which comes from treating the area as though it were a perimeter. Checking forwards: 12 × 12 = 144, which is the area given. Division undoes multiplication. Whenever the area is known and a side is not, divide.
The answer is B. Area is length × width, so finding a missing side means dividing rather than multiplying: 144 ÷ 12 = 12. The other side is 12 cm. Subtracting gives 132, which comes from treating the area as though it were a perimeter. Checking forwards: 12 × 12 = 144, which is the area given. Division undoes multiplication. Whenever the area is known and a side is not, divide.
An L-shaped room is made from two rectangles. The larger is 7 m by 12 m. The smaller, joined along one edge, is 3 m by 4 m. What is the total area of the floor?
Split the shape into the two rectangles and work them out separately. The larger is 7 × 12 = 84 m². The smaller is 3 × 4 = 12 m². Adding them gives 84 + 12 = 96 m². Multiplying the overall length by the overall width would count the corner that is not there, giving 160 m² — far too large. Sketch it, even roughly. Compound area questions are much harder to picture than to calculate.
The answer is B. Split the shape into the two rectangles and work them out separately. The larger is 7 × 12 = 84 m². The smaller is 3 × 4 = 12 m². Adding them gives 84 + 12 = 96 m². Multiplying the overall length by the overall width would count the corner that is not there, giving 160 m² — far too large. Sketch it, even roughly. Compound area questions are much harder to picture than to calculate.
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