Answer:
8 cm
Step-by-step explanation:
Use pythagorean theorem to find the height (a and b are equal):
[tex]a^2+b^2=16\sqrt{2}^2\\a^2+a^2=16\sqrt{2}^2\\2a^2=16\sqrt{2}^2\\2a^2=16(2)\\a^2=16\\a=\sqrt{16}\\a=4[/tex]
Area is half of the base times height. Base and height are equal for this triangle.
[tex]\frac{1}{2}(4)(4)\\\frac{1}{2}(16)\\8[/tex]
