Answer:
The area of the trapezoid is [tex]525\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of a isosceles trapezoid is equal to the area of two isosceles right triangles plus the area of a rectangle
step 1
Find the area of the isosceles right triangle
Remember that
In a isosceles right triangle the height is equal to the base of the triangle
we have
[tex]h=15\ cm[/tex]
so
[tex]b=15\ cm[/tex]
The area is equal to
[tex]A=\frac{1}{2}(b)(h)[/tex]
substitute the values
[tex]A=\frac{1}{2}(15)(15)=112.5\ cm^{2}[/tex]
step 2
Find the area of the rectangle
The area of the rectangle is equal to
[tex]A=LW[/tex]
we have
[tex]W=15\ cm[/tex] -----> is the height of the trapezoid
[tex]d=25\ cm[/tex] -----> the diagonal of the rectangle
Applying the Pythagoras Theorem
[tex]25^{2}=L^{2}+15^{2}\\L^{2}=25^{2}-15^{2} \\ L^{2} =400\\L=20\ cm[/tex]
The area of the rectangle is
[tex]A=(20)(15)=300\ cm^{2}[/tex]
step 3
Find the area of the trapezoid
[tex]A=2(112.5\ cm^{2})+300\ cm^{2}=525\ cm^{2}[/tex]
