What is the area of ΔABC such that b = 28 centimeters, c = 14 centimeters, and  measure of angle A equals 30 degrees question mark

98 centimeters2
169.741 centimeters2
193.654 centimeters2
196 centimeters2

To find the area of triangle \( \Delta ABC \) given the sides \( b = 28 \) cm, \( c = 14 \) cm, and the angle \( A = 30^\circ \), we can use the formula for the area of a triangle when two sides and the included angle are known:

\[
\text{Area} = \frac{1}{2} \times b \times c \times \sin(A)
\]

Substituting the given values:

\[
\text{Area} = \frac{1}{2} \times 28 \times 14 \times \sin(30^\circ)
\]

We know that \( \sin(30^\circ) = \frac{1}{2} \):

\[
\text{Area} = \frac{1}{2} \times 28 \times 14 \times \frac{1}{2}
\]

\[
\text{Area} = \frac{1}{2} \times 28 \times 14 \times \frac{1}{2} = 98 \text{ cm}^2
\]

Thus, the area of \( \Delta ABC \) is \( 98 \) square centimeters.

The correct answer is:

\[
\boxed{98 \text{ centimeters}^2}
\]

Would you like more details or have any questions?

Here are some related questions:

1. How do you derive the sine rule for calculating the area of a triangle?
2. What would be the area if angle A were 60 degrees instead of 30 degrees?
3. How does the area change if both sides \( b \) and \( c \) are doubled?
4. How can you find the area of a triangle if only one side and two angles are given?
5. What is the relationship between the area of a triangle and its perimeter?

**Tip:** When given two sides and the included angle in a triangle, the sine rule is a quick and effective way to find the area.

Learn how to calculate the area of triangle ABC using side lengths 28 cm and 14 cm, with angle A measuring 30 degrees. Detailed step-by-step solution using the sine rule for triangles. Suitable for high school students.

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