Question

Which of the following solutions are correct? A. Area of a right triangle with perpendicular and base of \(7\) and \(10\) cm respectively is \(35\text{ cm}^2\). B. Area of a square with a side measuring \(12\) cm is \(140\text{ cm}^2\). C. Area of a rectangle with sides \(11\) cm and \(70\) cm is \(770\text{ cm}^2\). D. Area of a circle with diameter \(28\) cm is \(606\text{ cm}^2\). E. Area of a circle with radius \(7\) cm is \(154\text{ cm}^2\).

• A. B, C and D only
• B. B, D and E only
• C. A, D and E only
• D. A, C and E only

Hint:

Use standard area formulas carefully: triangle \(\frac12 bh\), square \(a^2\), rectangle \(lb\), circle \(\pi r^2\).

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The goal is to evaluate five geometric area calculations and determine which of them are correct.

Step 2: Key Formula or Approach:
Let us use the standard geometric formulas for area:
• $\text{Area of a triangle} = \frac{1}{2} \times \text{base} \times \text{height}$
• $\text{Area of a square} = \text{side}^2$
• $\text{Area of a rectangle} = \text{length} \times \text{breadth}$
• $\text{Area of a circle} = \pi r^2$

Step 3: Detailed Explanation:
Let us compute the area for each scenario:
• Statement A: Base = 10 cm, perpendicular (height) = 7 cm. \[ \text{Area} = \frac{1}{2} \times 10 \times 7 = 35 \text{ cm}^2 \] This calculation is correct.
• Statement B: Side = 12 cm. \[ \text{Area} = 12^2 = 144 \text{ cm}^2 \neq 140 \text{ cm}^2 \] This calculation is incorrect.
• Statement C: Sides = 11 cm and 70 cm. \[ \text{Area} = 11 \times 70 = 770 \text{ cm}^2 \] This calculation is correct.
• Statement D: Diameter = 28 cm $\implies$ Radius ($r$) = 14 cm. \[ \text{Area} = \pi r^2 = \frac{22}{7} \times 14 \times 14 = 22 \times 2 \times 14 = 616 \text{ cm}^2 \neq 606 \text{ cm}^2 \] This calculation is incorrect.
• Statement E: Radius = 7 cm. \[ \text{Area} = \pi r^2 = \frac{22}{7} \times 7 \times 7 = 154 \text{ cm}^2 \] This calculation is correct.

Step 4: Final Answer:
Only calculations A, C, and E are correct. This corresponds to option (D).