Answer:
125
Step-by-step explanation:
In the diagram below; we have four triangles
Triangle
PRX; QSX; PQX; RSX
Let;
Δ PRX = [tex]T_1[/tex]
Δ QSX =[tex]T_2[/tex]
Δ PQX = [tex]T_3[/tex] = 20
Δ PQX = [tex]T_4[/tex] = 45
∴ [tex]T_1*T_2 =T_3*T_4[/tex]
[tex]T_1[/tex] is also parallel to [tex]T_2[/tex] : as such,[tex]T_1[/tex] = [tex]T_2[/tex]
∴[tex]T^2_{(1,2)}[/tex] = [tex]T_3*T_4[/tex]
[tex]T^2_{(1,2)}[/tex] = 20 × 45
[tex]T^2_{(1,2)}[/tex] = 900
[tex]T_{(1,2)}[/tex] = [tex]\sqrt{900}[/tex]
[tex]T_{(1,2)}[/tex] = 30
The area of the trapezoid is equal to T
T = [tex]T_1+T_2+T_3+T_4[/tex]
T = 30 + 30 + 20 + 45
T = 125
