Answer:
Explanation:
To find the area of a triangle, we can use the formula:
Area = (1/2) × base × height
In this case, we have three sides of the triangle given: 5, 3, and 4. To use these to find the area, we need to first determine which side is the base and what the corresponding height is.
We can see that the side with length 5 is opposite the biggest angle, so this is likely the hypotenuse. The other two sides, 3 and 4, must then be the other two legs of a right triangle, with one of them being the base and the other the height.
To determine which is which, we can use the Pythagorean theorem:
c^2 = a^2 + b^2
where c is the hypotenuse and a and b are the other two sides. In this case, we have:
5^2 = 3^2 + 4^2
25 = 9 + 16
So we have confirmed that 3 and 4 are indeed the legs of a right triangle, with 5 as the hypotenuse. We can use the Pythagorean theorem again to find the height:
a^2 + b^2 = c^2
b^2 = c^2 - a^2
b = sqrt(c^2 - a^2) (taking the positive square root because b is a length)
b = sqrt(5^2 - 3^2)
b = sqrt(16)
b = 4
So the height of the triangle is 4. We can now use the formula to find the area:
Area = (1/2) × base × height
Area = (1/2) × 3 × 4
Area = 6
Therefore, the area of the triangle is 6 square units.