Calculating Isosceles Triangle Area
This problem asks us to find the area of an isosceles triangle given the lengths of its two equal sides and the angle between them.
Understanding the Problem
- We have an isosceles triangle.
- The length of the two equal sides is 15 cm.
- The angle adjacent (between) these two equal sides is 30°.
- We need to find the area of the triangle.
Formula for Triangle Area
The area of a triangle can be calculated using the lengths of two sides and the sine of the angle included between them. The formula is:
Area = $\frac{1}{2}ab \sin(C)$
Where:
- 'a' and 'b' are the lengths of two sides.
- 'C' is the angle included between sides 'a' and 'b'.
Applying the Formula
In this specific problem:
- Side 'a' = 15 cm
- Side 'b' = 15 cm
- Angle 'C' = 30°
Let's substitute these values into the formula:
Area = $\frac{1}{2} \times 15 \text{ cm} \times 15 \text{ cm} \times \sin(30°)$
Step-by-Step Calculation
- First, calculate the product of the two sides: $15 \times 15 = 225$.
- Next, find the sine of the given angle: $\sin(30°) = \frac{1}{2}$.
- Now, multiply these results together with $\frac{1}{2}$: Area = $\frac{1}{2} \times 225 \text{ cm}^2 \times \frac{1}{2}$
- Combine the fractions: Area = $\frac{1 \times 225 \times 1}{2 \times 2} \text{ cm}^2$ Area = $\frac{225}{4} \text{ cm}^2$
- Perform the final division: Area = $56.25 \text{ cm}^2$
Conclusion
The calculated area of the isosceles triangle is 56.25 cm², which matches one of the provided options.
Similar Questions
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(Take $\pi = \frac{22}{7}$)
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