Answer:
24 in²
Step-by-step explanation:
The easy way:
The two legs, or shorter sides, of a right triangle form that triangle's base and height. Knowing that the area of a triangle is [tex]\frac{bh}{2}[/tex] (where b is the base and h is the height), we can use the 6 inch leg for the base and the 8 inch leg for the height to find an area of [tex]\frac{6(8)}{2}=\frac{48}{2}=24[/tex] in².
The harder but more general way
There's a nice formula for calculating the area of any triangle given its side lengths found by this Greek guy named Heron, and it's appropriately called Heron's formula:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)[/tex]
a, b, and c are the lengths of triangle, and s here is half the triangle's perimeter (also called the semi-perimeter), or mathematically:
[tex]s=\frac{a+b+c}{2}[/tex]
For our problem, let's pick a = 6, b = 8, and c = 10. This would give us
[tex]s=\frac{6+8+10}{2} =\frac{24}{2}=12[/tex]
Substituting that s back into Heron's formula, we get
[tex]A=\sqrt{12(12-6)(12-8)(12-10)}=\sqrt{12(6)(4)(2)}\\=\sqrt{72(8)}=\sqrt{576}=24[/tex]
So our area is 24 in²
