Answer:
96 square inches.
Step-by-step explanation:
From given picture we see that
BC=8 in
AD=10 in
Given that
AD=AB
Then AB=10 in
Apply Pythagorean theorem in triangle ABC to find AC
[tex](hypotenuse)^2=(base)^2+(perpendicular)^2[/tex]
[tex](AB)^2=(BC)^2+(AC)^2[/tex]
[tex](10)^2=(8)^2+(AC)^2[/tex]
[tex]100=64+(AC)^2[/tex]
[tex]100-64=(AC)^2[/tex]
[tex]36=(AC)^2[/tex]
take square root
[tex]6=AC[/tex]
Then area of triangle ABC [tex]=\frac{1}{2}\left(base\right)\left(altitude\right)[/tex]
[tex]=\frac{1}{2}\left(8\right)\left(6\right)=24[/tex]
There are total 4 congruent triangles.
Then total area of the given figure = 4(24)=96 square inches.
