What is the area of the quadrilateral?
(1 point)
○ 75 cm²
100 cm²
○ 125 cm²
○ 80 cm²
5 cm
4 cm
25 cm
I apologize for the confusion in my previous response. It seems I misunderstood your question.
To calculate the area of a quadrilateral given the lengths of three sides (a, b, and c) and an angle (θ) between two sides (a and b), we can use the formula:
Area = 0.5 * a * b * sin(θ) + 0.5 * c * (sqrt((a^2 + b^2 - 2*a*b*cos(θ))))
Plugging the values you provided:
a = 5 cm, b = 4 cm, c = 25 cm
Let's assume the angle between sides a and b is 90 degrees (for simplicity)
Area = 0.5 * 5 * 4 * sin(90) + 0.5 * 25 * (sqrt((5^2 + 4^2 - 2*5*4*cos(90))))
Area = 0.5 * 5 * 4 + 0.5 * 25 * (sqrt((25 + 16 - 2*5*4*0)))
Area = 10 + 0.5 * 25 * (sqrt(41))
Area = 10 + 12.5 * 6.40
Area = 10 + 80
Area = 90 cm²
Thus, the area of the quadrilateral with side lengths 5 cm, 4 cm, and 25 cm would be 90 cm². I hope this helps! Thank you for your patience.