Build confidence in measuring and comparing regions with these MCQs with answers and explanations for Class 8 Maths, Ganita Prakash Part 2, Chapter 7: Area. The questions move from rectangles and crossing paths to triangles, parallelograms, rhombuses and trapeziums. You will also compare equal-area shapes, examine how enlargement changes area and convert square units. Sketch the stated arrangements and identify the relevant base and perpendicular height before calculating.
Class 8 Maths Ganita Prakash Part 2 Chapter 7 MCQs with Answers
Set 1: Rectangles, Perimeters and Path Areas MCQs (Questions 1–5)
Q1. A rectangular rangoli has length 7 cm and width 4 cm. How many non-overlapping squares of side 1 cm exactly cover it?
[A]. 14
[B]. 11
[C]. 28
[D]. 22
Q2. Rectangle P measures 7 cm × 4 cm, and rectangle Q measures 8 cm × 3 cm. Which statement is correct?
[A]. They have equal perimeters, but P has greater area.
[B]. Q has both greater area and greater perimeter.
[C]. They have equal areas, but P has greater perimeter.
[D]. They have equal areas and equal perimeters.
Q3. A diagonal divides a rectangle of length 7 cm and width 4 cm into two triangles. What is the area of each triangle?
[A]. 7 cm²
[B]. 28 cm²
[C]. 14 cm²
[D]. 11 cm²
Q4. A rectangular park of length l and width w lies completely inside a larger rectangle of length L and width W. The region outside the park but inside the larger rectangle is a path. What is its area?
[A]. (L − l)(W − w)
[B]. LW − lw
[C]. 2(L + W − l − w)
[D]. LW + lw
Q5. Two straight paths cross at right angles inside a 14 m × 12 m rectangular plot. One path runs across the full 14 m length and the other across the full 12 m width. Each path is 1 m wide. What is their combined area?
[A]. 24 m²
[B]. 25 m²
[C]. 26 m²
[D]. 168 m²
Set 2: Scaling, Triangle Area and Perimeter MCQs (Questions 6–10)
Q6. A square and all the regions drawn inside it are enlarged in the same proportion so that its side length doubles. How does the area of each corresponding region change?
[A]. It becomes 2 times the original area.
[B]. It becomes half the original area.
[C]. It stays unchanged.
[D]. It becomes 4 times the original area.
Q7. In rectangle ABCD, DC = 5 units and AD = 4 units. Point X lies anywhere on the opposite side AB. What is the area of triangle XDC?
[A]. 20 square units
[B]. 10 square units
[C]. 9 square units
[D]. 5 square units
Q8. Several triangles share the same base BC. Their third vertices lie on a fixed line parallel to BC. Which statement about their areas is correct?
[A]. The triangle with the longest side has the greatest area.
[B]. Only the isosceles triangle has the greatest area.
[C]. Their areas cannot be compared.
[D]. All the triangles have equal areas.
Q9. A triangle has a fixed base BC, and its third vertex A lies on a fixed line parallel to BC. Which position of A gives the triangle the smallest perimeter?
[A]. Directly above C
[B]. Any position gives the same perimeter
[C]. Where the parallel line meets the perpendicular bisector of BC
[D]. Directly above B
Q10. In triangle ABC, BC = 5 units and the perpendicular height from A to BC is 3 units. Also, AC = 4 units. What is the perpendicular height from B to AC?
[A]. 3.75 units
[B]. 2.5 units
[C]. 4 units
[D]. 7.5 units
Set 3: Triangle Areas, Midpoints and Quadrilaterals MCQs (Questions 11–15)
Q11. Both diagonals of a rectangle are drawn. What fraction of the rectangle’s area is occupied by each of the four resulting triangles?
[A]. 1/8
[B]. 1/4
[C]. 1/2
[D]. 1/3
Q12. In triangle ABC, M is the midpoint of BC. What is the ratio of the areas of triangles ABM and ACM?
[A]. 2 : 1
[B]. 1 : 1
[C]. 1 : 2
[D]. 1 : 4
Q13. Triangle SUB is isosceles with SU = SB. The perpendicular SE meets UB at E. If triangle SEB has area 24 square units, what is the area of triangle SUB?
[A]. 72 square units
[B]. 24 square units
[C]. 48 square units
[D]. 12 square units
Q14. In triangle XYZ, M and N are the midpoints of XY and XZ respectively. What fraction of the area of triangle XYZ is the area of triangle XMN?
[A]. 1/4
[B]. 1/8
[C]. 3/4
[D]. 1/2
Q15. A diagonal AC of a convex quadrilateral ABCD is 22 cm long. The perpendicular distances of B and D from AC are each 3 cm. What is the area of the quadrilateral?
[A]. 33 cm²
[B]. 66 cm²
[C]. 44 cm²
[D]. 132 cm²
Set 4: Composite Shapes, Parallelograms and Rearrangement MCQs (Questions 16–20)
Q16. Rectangle ABCD has AB = 18 cm and BC = 10 cm. Point E lies on AB with AE = 10 cm and EB = 8 cm. Point F lies on AD with AF = 6 cm and FD = 4 cm. What is the area of quadrilateral DFEC?
[A]. 180 cm²
[B]. 140 cm²
[C]. 110 cm²
[D]. 70 cm²
Q17. A parallelogram has a base of 7 cm and a corresponding perpendicular height of 4 cm. What is its area?
[A]. 11 cm²
[B]. 14 cm²
[C]. 22 cm²
[D]. 28 cm²
Q18. One side of a parallelogram is 5 cm long. The perpendicular distance from the opposite side to this side is 4.8 cm. What is its area?
[A]. 24 cm²
[B]. 9.8 cm²
[C]. 19.6 cm²
[D]. 12 cm²
Q19. A rectangle and a non-rectangular parallelogram both have adjacent side lengths 5 cm and 4 cm. Which has the greater area?
[A]. Their areas are always equal.
[B]. The answer depends only on their perimeters.
[C]. The parallelogram always has the greater area.
[D]. The rectangle has the greater area.
Q20. A shape is cut into pieces and all the pieces are rearranged without overlap to make another shape. Which quantity must remain unchanged?
[A]. Its longest side
[B]. Its perimeter
[C]. Its area
[D]. Its number of sides
Set 5: Rhombus and Trapezium Areas MCQs (Questions 21–25)
Q21. The diagonals of a rhombus are 20 cm and 15 cm. What is its area?
[A]. 150 cm²
[B]. 75 cm²
[C]. 300 cm²
[D]. 175 cm²
Q22. A rhombus has diagonals d₁ and d₂. Which rectangle has the same area as the rhombus?
[A]. A rectangle with sides d₁ and d₂/2
[B]. A rectangle with sides 2d₁ and d₂
[C]. A rectangle with sides d₁ and d₂
[D]. A rectangle with sides d₁/2 and d₂/2
Q23. A trapezium has parallel sides 24 m and 36 m. Their perpendicular distance is 14 m. What is its area?
[A]. 168 m²
[B]. 840 m²
[C]. 420 m²
[D]. 336 m²
Q24. A trapezium has parallel vertical sides of lengths 14 inches and 6 inches. The perpendicular distance between them is 10 inches. What is its area?
[A]. 84 in²
[B]. 40 in²
[C]. 200 in²
[D]. 100 in²
Q25. Two identical trapeziums each have parallel sides a and b and height h. One is rotated through 180° and joined to the other along a matching non-parallel side to form a parallelogram. Taking the joined parallel sides as the base, what are its base and height?
[A]. Base a + b and height 2h
[B]. Base a − b and height h
[C]. Base a and height b
[D]. Base a + b and height h
Set 6: Area Ratios, Measurements and Unit Conversions MCQs (Questions 26–30)
Q26. A regular hexagon is divided into six equal-area equilateral triangles by joining its centre to its vertices. Three adjacent triangles form a trapezium, one remains a triangle, and the other two form a rhombus. What is the area ratio trapezium : triangle : rhombus?
[A]. 1 : 1 : 1
[B]. 3 : 2 : 1
[C]. 3 : 1 : 2
[D]. 2 : 1 : 3
Q27. An A4 sheet measures 21 cm by 29.7 cm. What is its area?
[A]. 1247.4 cm²
[B]. 50.7 cm²
[C]. 62.37 cm²
[D]. 623.7 cm²
Q28. Given that 1 inch = 2.54 cm, what is 1 square inch in square centimetres?
[A]. 6.4516 cm²
[B]. 2.54 cm²
[C]. 25.4 cm²
[D]. 5.08 cm²
Q29. Given that 1 in² = 6.4516 cm², how many square inches are equal to 161.29 cm²?
[A]. 25 in²
[B]. 20 in²
[C]. 40 in²
[D]. 10 in²
Q30. Given that 1 foot = 12 inches, how many square inches are there in 1 square foot?
[A]. 120 in²
[B]. 144 in²
[C]. 24 in²
[D]. 12 in²
Check Heights, Overlaps and Square Units
Revisit any question where you used a sloping side as the height or counted an overlapping region twice. Draw the perpendicular height and mark the pieces being added or removed. For unit conversions, square the length conversion factor. Keep area and perimeter calculations separate, since equal perimeters do not guarantee equal areas.
