Answer:
The area of trapezoid PQRS is 125 square units
Step-by-step explanation:
The picture of the question in the attached figure
we know that
If trapezoid PQRS with parallel sides PQ and RS is divided into four triangles by its diagonals PR and QS , intersecting at X, then the area of triangle PSX is equal to that of triangle QRX, and the product of the areas of triangle PSX and triangle QRX is equal to that of triangle PQX and triangle RSX
Let
A_1 ----> the area of triangle PSX
A_2----> the area of triangle QRX
A_3 ---> the area of triangle PQX
A_4 ---> the area of triangle RSX
[tex]A_1*A_2=A_3*A_4[/tex]
[tex]A_1=A_2[/tex]
so
[tex]A_1^2=A_3*A_4[/tex]
we have
[tex]A_3=20\ units^2\\A_4=45\ units^2[/tex]
substitute
[tex]A_1^2=(20)(45)\\A_1^2=900\\A_1=30\ units^2[/tex]
The area of trapezoid is equal to
[tex]A=A_1+A_2+A_3+A_4[/tex]
substitute
[tex]A=30+30+20+45=125\ units^2[/tex]
