Answer:
The area of the the trapezoid is 40.2cm.
Step-by-step explanation:
check the attached document for the assumed figure of the trapezoid.
First we use cosine rule to determine the angle at C or ∠BCD.
Applying the formula; c²=b²+d²-2bdCos C
9²=8²+7²-2(8)(7) Cos C
81=113-112 Cos C
-32= -112 Cos C
Cos C=32/112= 0.2857
C= Arc Cos 0.2857=73.398°
Next we find the height of the trapezoid /BE/.
And since BEC is a right angled triangle, we use trig ratios.
Sin C= opposite/hypotenuse
sin 73.398°= h/7
so that height= 7 sin 73.398°= 6.7cm
and for /EC/ ⇒Cos 73.398°=Adjacent/Hypotenuse=x/7
x=7 Cos 73.398 =2.0cm
x=/DF/=/EC/=2.0cm.
/AB/= /DC/ - (/DF/+/EC/)
/AB/=8 - (2+2) = 4cm
Hence, Area of trapezoid ABCD=1/2(a+b)h
Area ABCD= 1/2(4+8)cm*6.7cm
Area ABCD= 40.2cm²
