Answer:
6.1 cm²
Step-by-step explanation:
To find the area of triangle DEF, given two sides and the included angle, we can use the formula for the area of a triangle when two sides and the included angle are known. This formula is:
[tex]Area= \dfrac{1}{2}ab\sin(C)[/tex]
In this formula, a and b are the lengths of the two sides, and C is the measure of the included angle in degrees.
Given e = 1.4 cm, f = 9.1 cm, and [tex]\angle D = 109[/tex] degrees, we can identify a = 1.4 cm, b = 9. cm, and C = 109 degrees. Plugging these values into the formula gives us:
[tex]Area = \frac{1}{2} \times 1.4 \times 9.1 \times \sin(109^\circ)[/tex]
We need to use a calculator to find the sine of 109 degrees and compute the area.
[tex]Area} = \frac{1}{2} \times 1.4 \times 9.1 \times \sin(109^\circ)\\\\ Area \approx \frac{1}{2} \times 1.4 \times 9.1 \times 0.953 \\\\Area \approx \frac{1}{2} \times 1.4 \times 9.1 \times 0.953 \\\\Area \approx 0.7 \times 9.1 \times 0.953 \\\\Area \approx 6.10823[/tex]
