A triangular field with base 40 m and height 30 m shares a side with a rectangle of length 40 m and breadth 25 m. Find the combined area and percentage of the triangle’s area in the total.
- (a)1,450 m² and 24.5%
- (b)2,450 m² and 25.5%
- (c)1,600 m² and 37.5%
- (d)2,500 m² and 25%
Answer
Why
Correct — C.
The two figures meet along a side without overlapping, so their areas add.
Triangle: ½ × 40 × 30 = 600 m²
Rectangle: 40 × 25 = 1,000 m²
Combined: 600 + 1,000 = 1,600 m²
Triangle's share: 600 ÷ 1,600 × 100 = 37.5% → option (c)
Why the others are wrong
- (a)1,450 m² and 24.5% — 1,450 m² is 150 short of 600 + 1,000 = 1,600 m². And 24.5% of 1,450 is about 355 m², not the triangle's 600 m².
- (b)2,450 m² and 25.5% — 2,450 m² is 850 more than 600 + 1,000 = 1,600 m². And 25.5% of 2,450 is about 625 m², not the triangle's 600 m².
- (d)2,500 m² and 25% — 2,500 m² with 25% would make the triangle 625 m², but ½ × 40 × 30 = 600 m². The total also overshoots 1,600 m².
Concept
The area of a triangle is ½ × base × height, and of a rectangle length × breadth.
When two figures share a side and lie on opposite sides of it, the combined area is simply the sum. The shared side is a boundary, not a region.
A part's percentage = part ÷ whole × 100, and here the whole is the combined area.
A faster percentage: 600⁄1,600 reduces to 3⁄8, and 3⁄8 = 37.5%.
Key facts
- Area of a triangle = ½ × base × height
- Area of a rectangle = length × breadth
- 3⁄8 = 37.5%
Study next
Common traps
- Forgetting the ½ in the triangle's area, which makes it 1,200 m²
- Dividing the triangle's area by the rectangle's (600 ÷ 1,000 = 60%) instead of by the combined area
14 Sep 2025, 12:30, Quant Q.21 builds the composite by subtraction instead: a 28 m square field (784 m²) minus a 616 m² pond leaves the keyed 168 m².
21 Sep 2025, 16:00, Quant Q.11 uses the same ½ × base × height on a right triangle with legs 5 m and 12 m, keyed 30 m².
Related PYQs
No directly related past PYQ was found.