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

Check statement A. Area of a right triangle is: \[ \frac{1}{2}\times \text{base}\times \text{height}. \] \[ =\frac{1}{2}\times10\times7=35. \] So A is correct. Check statement B. Area of square is: \[ \text{side}^2. \] \[ 12^2=144. \] So area is \(144\text{ cm}^2\), not \(140\text{ cm}^2\). Thus B is incorrect. Check statement C. Area of rectangle is: \[ \text{length}\times \text{breadth}. \] \[ 11\times70=770. \] So C is correct. Check statement D. Diameter of circle is \(28\) cm. So radius is: \[ 14\text{ cm}. \] Area is: \[ \pi r^2=\frac{22}{7}\times14\times14. \] \[ =616\text{ cm}^2. \] So D is incorrect because it says \(606\text{ cm}^2\). Check statement E. Radius is \(7\) cm. Area is: \[ \pi r^2=\frac{22}{7}\times7\times7. \] \[ =154\text{ cm}^2. \] So E is correct. Therefore, the correct statements are: \[ A,\ C,\ E. \] Hence, the correct answer is option (D).