Question

The base of a triangle is increased in length by 20% and its height reduced by 20%. How does its area change?

• A. reduced by 4%
• B. increased by 4%
• C. does not change
• D. reduced by 4.166%
• E. increases by 4.166 %

Answer 1

The Correct Option is A

Step 1: Understand the formula for the area of a triangle.
The area of a triangle is given by the formula:
\( \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \)

Step 2: Analyze the effect of the changes on the base and height.
- The base of the triangle is increased by 20%, so the new base becomes \( 1.20 \times \text{Base} \).
- The height of the triangle is reduced by 20%, so the new height becomes \( 0.80 \times \text{Height} \).

Step 3: Calculate the new area.
The new area of the triangle will be:
\( \text{New Area} = \frac{1}{2} \times (1.20 \times \text{Base}) \times (0.80 \times \text{Height}) \)
\( \text{New Area} = \frac{1}{2} \times 1.20 \times 0.80 \times \text{Base} \times \text{Height} \)
\( \text{New Area} = 0.96 \times \text{Area} \)

Step 4: Conclusion.
The new area is 96% of the original area, meaning the area is reduced by 4%.

Final Answer:
The correct option is (A): reduced by 4%.