28.7cm²
The sketch of the parallelogram is attached to this response.
As shown in the sketch,
h is the height of the parallelogram
ADC is 125°
AD = 5cm
CD = 7cm
Also
Since the adjacent angles of a parallelogram are supplementary (add up to 180°), it means that;
=> ADC + BCD = 180°
=> 125° + BCD = 180°
=> BCD = 180° - 125°
=> BCD = 55°
The area (A) of a parallelogram is given by;
A = b x h ----------(i)
Where
b = base of the parallelogram
h = height of the parallelogram
From the sketch,
b = CD = 7cm
h can be found by using the sine trigonometric function as follows
sin BCD = [tex]\frac{h}{BC}[/tex]
=> sin 55° = [tex]\frac{h}{5}[/tex]
=> h = 5 sin 55°
=> h = 5 x 0.8192
=> h = 4.096cm
Now, substitute the values of h and b into equation (i) as follows;
A = 7 x 4.096
A = 28.672
A ≅ 28.7 (to one decimal place)
Therefore, the area of the parallelogram is 28.7cm²
