Class 6 Area of Combined Shapes — practice questions with answers
Mensuration · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. This shape is made of two rectangles: one 5 cm by 3 cm and the other 4 cm by 2 cm. What is its total area?
A23 sq cm
B28 sq cm
C120 sq cm
D14 sq cm
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Answer: A) 23 sq cm
Area of first rectangle = 5 × 3 = 15 sq cm. Area of second = 4 × 2 = 8 sq cm. Total = 15 + 8 = 23 sq cm. (14 is just 5 + 3 + 4 + 2, a sum of lengths, not an area.)
2. What is the perimeter of this shape? Two sides are not labelled — work them out first.
A50 cm
B34 cm
C30 cm
D38 cm
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Answer: D) 38 cm
Missing sides: 10 − 6 = 4 cm (step across) and 9 − 5 = 4 cm (step down). Perimeter = 6 + 4 + 4 + 5 + 10 + 9 = 38 cm. (30 leaves out the two missing sides.)
3. The table gives the sizes of the rooms in Anil's flat. What is the total floor area of the three rooms?
A36 sq m
B21 sq m
C38 sq m
D42 sq m
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Answer: C) 38 sq m
Bedroom 4 × 3 = 12, hall 5 × 4 = 20, kitchen 3 × 2 = 6. Total = 12 + 20 + 6 = 38 sq m. (21 just adds all the lengths and breadths.)
4. A bookshelf's back panel is a 90 cm × 60 cm rectangle with a 30 cm × 20 cm slot cut out for wires. What is the panel's area?
A4,800 sq cm
B4,200 sq cm
C6,000 sq cm
D5,350 sq cm
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Answer: A) 4,800 sq cm
Panel = 90 × 60 = 5,400 sq cm. Slot = 30 × 20 = 600 sq cm. Area = 5,400 − 600 = 4,800 sq cm. (5,350 subtracts 30 + 20 = 50.)
5. Plan A: tile an L-shaped floor (5 m × 4 m plus 3 m × 2 m) at ₹80 per sq m. Plan B: carpet only the 5 m × 4 m part at ₹100 per sq m. How much more does Plan A cost?
A₹80
B₹480
C₹120
D₹600
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Answer: A) ₹80
Plan A: area 20 + 6 = 26 sq m, cost 26 × 80 = ₹2080. Plan B: 20 × 100 = ₹2000. Difference = ₹80.