Final answer:
The correct answer is Option E. To find the area of triangle EFG, we can use the formula for the area of a triangle, which is 1/2 × base × height. In this case, we need to find the height using trigonometry. Once we have the height, we can substitute the values into the area formula to calculate the area of triangle EFG.
Step-by-step explanation:
To find the area of triangle EFG, we can use the formula for the area of a triangle, which is: Area = 1/2 × base × height. In this case, the base is e = 47 cm and the height is the perpendicular distance from E to the line containing FG. To find the height, we can use trigonometry. Since we know angles E and F, we can find angle G using the fact that the sum of the angles in a triangle is 180 degrees. Then, we can use the sine of angle G to find the height. Finally, we can substitute the values into the area formula to calculate the area of triangle EFG.
Let's calculate the height first:
Angle G = 180 - Angle E - Angle F = 180 - 34 - 12 = 134 degrees
Sine of angle G = Opposite/Hypotenuse = height/e
height = e * sine(G) = 47 * sine(134) ≈ 47 * 0.938 = 44.086 cm
Now, let's substitute the values into the area formula:
Area = 1/2 * base * height = 1/2 * 47 * 44.086 = 1035.451 cm²
Rounded to the nearest square cm, the area of triangle EFG is approximately 1035 cm².