Answer:
Step-by-step explanation:
Surface area = lateral area + 2(area of base)
Lateral area = perimeter of base * height.
Because it is a isosceles right triangle, both sides are equal.
[tex]x^{2} +x^{2}[/tex] = 72
2[tex]x^{2}[/tex] = 72. Divide both sides by 2
[tex]x^{2}[/tex] = 36. Square both sides.
x = 6.
So the perimeter of the base = 6 + 6 +[tex]\sqrt{72}[/tex] = 20.485281374239
Lateral area = 20.485281374239 * 7 = 143.397 [tex]cm^{2}[/tex]
Area of base is (1/2)base * height.
(1/2)(6)(6) = 18
Using the surface area formula
surface area = 143.397 + 2(18) = 179.4 [tex]cm^{3}[/tex]
