Given triangle DEF with sides $d$ and $e$ and included angle $F$, what is the formula for its area?

• A. $\frac{1}{2}desinF$
• B. $desinF$
• C. $\frac{1}{2}dfsinE$
• D. $\frac{1}{2}decosF$

Answer: (A)

Verified step by step guidance

1. Recall that the area of a triangle can be found using the formula involving two sides and the included angle: \(\text{Area} = \frac{1}{2} \times \text{(side 1)} \times \text{(side 2)} \times \sin(\text{included angle})\).
2. Identify the two sides given in the problem: sides \(d\) and \(e\) of triangle DEF.
3. Identify the included angle between these two sides, which is angle \(F\).
4. Substitute the known sides and included angle into the formula: \(\text{Area} = \frac{1}{2} \times d \times e \times \sin(F)\).
5. This formula calculates the area by taking half the product of the two sides and the sine of the included angle, which gives the height component relative to the base.