7TH MATHS AREA AND PERIMETER OF THE PARALLELOGRAM

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Class 7 Maths – Perimeter and Area of a Parallelogram Master Quiz

1. What is the standard formula for the perimeter of a parallelogram?

a) base + height b) 2 × (sum of adjacent sides) c) base × height d) side × side

Correct Answer: b) 2 × (sum of adjacent sides)

Explanation: A parallelogram has two pairs of equal opposite sides. Therefore, its perimeter is the distance around the outside, calculated as 2 × (length + breadth) or 2 × (sum of adjacent sides), exactly like a rectangle!

2. A parallelogram has adjacent sides of 5 cm and 7 cm. What is its total perimeter?

a) 24 cm b) 35 cm c) 12 cm d) 14 cm

Correct Answer: a) 24 cm

Explanation: Using the perimeter formula: 2 × (5 cm + 7 cm) = 2 × (12 cm) = 24 cm.

3. The adjacent sides of a parallelogram are 8.5 cm and 4.5 cm. Find its perimeter.

a) 13 cm b) 26 cm c) 18 cm d) 38.25 cm

Correct Answer: b) 26 cm

Explanation: Sum of the adjacent sides = 8.5 + 4.5 = 13.0 cm. Perimeter = 2 × 13 cm = 26 cm. (Notice that 38.25 cm would be the area if these were base and height, but they are adjacent sides!)

4. What is the correct formula for finding the Area of a parallelogram?

a) base + height b) ½ × base × height c) base × height d) 2 × (base + height)

Correct Answer: c) base × height

Explanation: The area of a parallelogram is simply its base multiplied by its perpendicular height (Area = b × h). Option 'b' is the formula for a triangle!

5. A parallelogram has a base of 10 cm and a corresponding height of 5 cm. What is its area?

a) 15 cm² b) 25 cm² c) 50 cm² d) 100 cm²

Correct Answer: c) 50 cm²

Explanation: Area = base × height. Therefore, 10 cm × 5 cm = 50 cm².

6. The area of a parallelogram is 72 cm² and its base is 8 cm. What must be its height?

a) 8 cm b) 9 cm c) 64 cm d) 12 cm

Correct Answer: b) 9 cm

Explanation: Since Area = base × height, you can find the missing height by dividing the Area by the base. Height = 72 cm² ÷ 8 cm = 9 cm.

7. If the area of a parallelogram is 144 cm² and its height is 12 cm, find the length of its base.

a) 10 cm b) 12 cm c) 15 cm d) 18 cm

Correct Answer: b) 12 cm

Explanation: Base = Area ÷ height. Base = 144 cm² ÷ 12 cm = 12 cm.

8. What happens to the area of a parallelogram if you double the length of its base, but keep the height the same?

a) It becomes half b) It stays exactly the same c) It doubles d) It quadruples (4 times bigger)

Correct Answer: c) It doubles

Explanation: Area is directly proportional to the base. If you multiply the base by 2, the total product (Area = base × height) is also multiplied by 2.

9. Which of these regular shapes shares the exact same basic area formula (Area = base × height) as a parallelogram?

a) Square b) Triangle c) Circle d) Rectangle

Correct Answer: d) Rectangle

Explanation: A rectangle is actually a special type of parallelogram! A rectangle's area is length × breadth, which is conceptually exactly the same as base × height.

10. The area of a parallelogram does NOT depend on which of the following?

a) The length of its base b) Its perpendicular height c) The length of its slanted side d) It depends on all of the above

Correct Answer: c) The length of its slanted side

Explanation: The slanted side is only used to calculate the perimeter. For Area, only the horizontal base and the straight perpendicular height are needed!