Answer:
300 square units
Step-by-step explanation:
Let M be the midpoint of BC. Then AM =20 is the altitude. Let x represent the length BM=MC, and let y represent the length AB=AC. Then the perimeter is ...
2x +2y = 80
x +y = 40 . . . . divide by 2 . . . . . [eq A]
The Pythagorean theorem tells us ...
x^2 + 20^2 = y^2 . . . . . . . y is the hypotenuse of right triangle AMC
Rearranging, we have ...
y^2 -x^2 = 400
(y -x)(y +x) = 400
(y -x)·40 = 400
y -x = 10. . . . . . . . . [eq B]
Subtracting [eq B] from [eq A], we find ...
(x +y) -(y -x) = (40) -(10)
2x = 30
x = 15
The area of interest is 20x, so is ...
A = 20·x = 20·15 = 300 . . . . square units
