Question

Two sides of a plot measure 32 m and 24 m and the angle between them a perfect right angle. The other two sides measure 25 m each and the other three angles are not right angles. What is the area of the plot (in m\(^2\))?

Answer 1

Correct Answer: 3

Concept: Divide the figure into:

• One right triangle
• One isosceles triangle

Step 1: Right triangle area.
\[ \text{Sides} = 32, 24 \] \[ \text{Area} = \frac{1}{2} \times 32 \times 24 = 384 \]
Step 2: Remaining triangle.
The remaining triangle has sides: \[ 25, 25, \text{base} = \sqrt{32^2 + 24^2} = 40 \]
Step 3: Area of isosceles triangle.
\[ \text{Height} = \sqrt{25^2 - 20^2} = \sqrt{625 - 400} = 15 \] \[ \text{Area} = \frac{1}{2} \times 40 \times 15 = 300 \]
Step 4: Total area.
\[ 384 + 300 = 684 \]
Step 5: Option analysis.

• (A) Incorrect $\times$
• (B) Incorrect $\times$
• (C) Correct \checkmark
• (D) Incorrect $\times$
• (E) Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (C).