Find the area of the triangle by 16ft, and 62ft
Not Drawn to scale
496 ft
248ft
79ft
37ft
496 ft^2
To find the area of a triangle, we need the lengths of two sides and the included angle. However, in this case, we only have the lengths of two sides.
To determine the area of a triangle using only the lengths of two sides, we can use Heron's formula. This formula states that the area of a triangle with side lengths a, b, and c, where s is the semi-perimeter (s = (a + b + c)/2), is given by:
Area = √(s(s-a)(s-b)(s-c))
In our case, we have two sides of lengths 16ft and 62ft. We need to determine the length of the third side to calculate the area.
To find the third side length, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.
Given the side lengths of 16ft and 62ft, the third side length must satisfy the following inequality:
16 + 62 > third side
78 > third side
Therefore, the third side must be less than 78ft.
Since we do not have the exact value of the third side, we cannot find the accurate area using Heron's formula. The options provided (496ft, 248ft, 79ft, and 37ft) are not the correct answer, as they do not match any possible area values for the given side lengths.
To find the area accurately, we would need the exact length of the third side or additional information about the triangle.
To find the area of a triangle, we need to use the formula:
Area = (base × height) / 2.
In this case, the base is 16ft and the height is 62ft.
Using the formula, we can calculate the area as follows:
Area = (16ft × 62ft) / 2
= 992ft² / 2
= 496ft².
Therefore, the area of the triangle is 496ft².