1. What is the area of a parallelogram with a base of 10 cm and a height of 3 cm?
- A30 cm²
- B13 cm²
- C15 cm²
- D60 cm²
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Answer: A) 30 cm²
The area is calculated as Base × Height = 10 cm × 3 cm = 30 cm².
Class 9 Areas of Parallelograms and Triangles — practice questions with answers
Geometry · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. Two figures are said to be 'on the same base and between the same parallels' if they have a common base and their opposite sides (or vertices) lie on which of the following?
- AA line parallel to the base
- BA line perpendicular to the base
- CThe base itself
- DTwo intersecting lines
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Answer: A) A line parallel to the base
Figures on the same base and between the same parallels have their other side or vertex on a line parallel to the base. This guarantees they share the same height.
3. If two triangles have equal areas and equal bases, then their corresponding heights are:
- AEqual
- BIn the ratio 1:2
- CAlways different
- DIn the ratio 2:1
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Answer: A) Equal
Area = × base × height. If areas and bases are equal, then heights must also be equal.
4. A parallelogram and a triangle stand on the same base of 16 cm and between the same parallels which are 9 cm apart. Find the area of the triangle in cm².
- A65
- B72
- C79
- D144
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Answer: B) 72
Triangle area = × base × height = × 16 × 9 = 72 cm². (This is also half of the parallelogram's area 144 cm².)
5. A parallelogram ABCD and a rectangle ABEF are on the same base AB and have equal areas. Which of the following is correct?
- AThe perimeter of the parallelogram is greater than the perimeter of the rectangle
- BThe perimeter of the rectangle is greater than the perimeter of the parallelogram
- CBoth perimeters are always equal
- DThe parallelogram has the smaller area
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Answer: A) The perimeter of the parallelogram is greater than the perimeter of the rectangle
Since the areas are equal and bases are equal, they are between the same parallels (equal height). The slant sides of the parallelogram are longer than the equal perpendicular sides of the rectangle, so the parallelogram has the greater perimeter. (Areas remain equal, so the last option is false.)
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