CBSE Class 7 Mathematics Perimeter and Area Assignment Set 04

Fill the gap.

Q1. Area of a triangle is ________
Answer: \(\frac{1}{2} \times \text{Base} \times \text{Height}\)
In simple words: The area of a triangle is half the product of its base and corresponding altitude.

Exam Tip: Remember to include the fraction \(\frac{1}{2}\) when calculating triangle area.

Q2. Area of Equilateral triangle of side 4 cm is ________
Answer: Area of an equilateral triangle = \(\frac{\sqrt{3}}{4} \times (\text{side})^2\)
Given side = 4 cm
Area = \(\frac{\sqrt{3}}{4} \times 4^2 = \frac{\sqrt{3}}{4} \times 16 = 4\sqrt{3} \text{ cm}^2\)
In simple words: Substitute the side length into the standard formula for an equilateral triangle.

Exam Tip: Memorize the formula \(\frac{\sqrt{3}}{4}a^2\) for quick calculation of equilateral triangle areas.

Q3. Area of a rectangle of side 4 cm x 3 cm is ________
Answer: Area of rectangle = \(\text{Length} \times \text{Breadth}\)
Area = \(4 \text{ cm} \times 3 \text{ cm} = 12 \text{ cm}^2\)
In simple words: Multiply the length and width of the rectangle.

Exam Tip: Area is always expressed in square units (e.g., \(\text{cm}^2\)).

Q4. Area of a Square of side 5 cm is ________
Answer: Area of square = \((\text{side})^2\)
Area = \(5^2 = 25 \text{ cm}^2\)
In simple words: Multiply the side length by itself.

Exam Tip: For any square, squaring the side gives the total surface area.

Q5. Diagonal of a square of side 2 cm is ________
Answer: Diagonal of a square = \(\text{side} \times \sqrt{2}\)
Given side = 2 cm
Diagonal = \(2\sqrt{2} \text{ cm}\)
In simple words: The diagonal is found by multiplying the side length by \(\sqrt{2}\).

Exam Tip: This comes directly from Pythagoras theorem applied to the right-angled triangle formed by two adjacent sides and the diagonal.

Q6. Perimeter of a triangle of side 3, 4, 5 cm is ________
Answer: Perimeter = Sum of all three sides
Perimeter = \(3 + 4 + 5 = 12 \text{ cm}\)
In simple words: Add the lengths of all outer boundaries together.

Q7. Perimeter of a square if its area is \(36 \text{ cm}^2\) is ________
Answer: Area of square = \(36 \text{ cm}^2\)
Side of square = \(\sqrt{36} = 6 \text{ cm}\)
Perimeter = \(4 \times \text{side} = 4 \times 6 = 24 \text{ cm}\)
In simple words: First find the side length by taking the square root of the area, then multiply by 4.

Exam Tip: Never confuse area units with perimeter units.

Q8. Perimeter of a rectangle of length 10 cm and area \(60 \text{ cm}^2\) is ________
Answer: Area = \(\text{Length} \times \text{Breadth}\)
\(60 = 10 \times \text{Breadth}\)
Breadth = \(\frac{60}{10} = 6 \text{ cm}\)
Perimeter = \(2 \times (\text{Length} + \text{Breadth}) = 2 \times (10 + 6) = 2 \times 16 = 32 \text{ cm}\)
In simple words: Find the missing breadth using the area, then calculate the perimeter.

Exam Tip: Always write down the formula before substituting values.

Q9. Area of a circle of diameter 5 cm ________
Answer: Diameter \(d = 5 \text{ cm}\), so radius \(r = \frac{5}{2} = 2.5 \text{ cm}\)
Area = \(\pi r^2 = \frac{22}{7} \times (2.5)^2 = \frac{22}{7} \times 6.25 = \frac{137.5}{7} \approx 19.64 \text{ cm}^2\)
In simple words: Find the radius from the diameter and apply the circle area formula.

Exam Tip: Use \(\pi \approx \frac{22}{7}\) or \(3.14\) for calculations.

Q10. Circumference of a circle if area is \(154 \text{ cm}^2\) is ________
Answer: Area = \(\pi r^2 = 154\)
\(\frac{22}{7} \times r^2 = 154\)
\(r^2 = \frac{154 \times 7}{22} = 7 \times 7 = 49\)
\(r = 7 \text{ cm}\)
Circumference = \(2\pi r = 2 \times \frac{22}{7} \times 7 = 44 \text{ cm}\)
In simple words: Determine the radius from the given area, then use it to find the circumference.

Exam Tip: Recognizing standard multiples like 154 for areas with radius 7 saves time.

Q11. Area of a parallelogram if base is 10 cm and height 5 cm
Answer: Area of parallelogram = \(\text{Base} \times \text{Height}\)
Area = \(10 \text{ cm} \times 5 \text{ cm} = 50 \text{ cm}^2\)
In simple words: Multiply the base and the perpendicular height.

Q12. Circumference of a circle is 44 cm. Its area is ________
Answer: Circumference = \(2\pi r = 44\)
\(2 \times \frac{22}{7} \times r = 44\)
\(\frac{44}{7} \times r = 44\)
\(r = 7 \text{ cm}\)
Area = \(\pi r^2 = \frac{22}{7} \times 7^2 = \frac{22}{7} \times 49 = 154 \text{ cm}^2\)
In simple words: Find the radius from the circumference, then calculate the area.

Exam Tip: A circle with circumference 44 cm always has an area of \(154 \text{ cm}^2\).

Q13. If area of a rectangle is \(7256 \text{ m}^2\). In hectares, this will be ________
Answer: We know that \(1 \text{ hectare} = 10,000 \text{ m}^2\)
Area in hectares = \(\frac{7256}{10000} = 0.7256 \text{ hectares}\)
In simple words: Divide the area in square meters by 10,000 to convert to hectares.

Exam Tip: Shifting the decimal point four places to the left converts \(\text{m}^2\) to hectares.

Q14. Base of a llgm = \(\frac{\text{Area}}{\text{________}}\)
Answer: Height
In simple words: Base is calculated by dividing the area of a parallelogram by its height.

Exam Tip: Derived from the formula: Area = Base \(\times\) Height.

Q15. The area of a llgm ABCD is \(1518 \text{ m}^2\). The altitude drawn from D on AB is \(25.3 \text{ m}\). The length of AB is ________
Answer: Area of parallelogram = \(\text{Base} \times \text{Height}\)
\(1518 = \text{AB} \times 25.3\)
\(\text{AB} = \frac{1518}{25.3} = 60 \text{ m}\)
In simple words: Divide the total area by the given altitude to find the base length AB.

Exam Tip: Double-check decimal division by multiplying 60 by 25.3 to verify 1518.