find the area of a triangle where sides are 25, 25 and 14
This is an Isoceles triangle whose base
is 14 units long.
(14/2)^2 + h^2 = (25)^2,
h^2 = 625 - 49 = 576,
h = 24 units.
A = bh/2 = 14*24/2 = 168 sq. units.
To find the area of a triangle, we can use Heron's formula.
Heron's formula states that the area (A) of a triangle with sides a, b, and c can be calculated using the following formula:
A = √(s(s - a)(s - b)(s - c))
Where s is the semi-perimeter of the triangle, calculated as:
s = (a + b + c) / 2
In this case, the sides of the triangle are given as 25, 25, and 14.
Let's first calculate the semi-perimeter (s):
s = (25 + 25 + 14) / 2
= 64 / 2
= 32
Now we can calculate the area (A) using Heron's formula:
A = √(32(32 - 25)(32 - 25)(32 - 14))
Simplifying this expression:
A = √(32(7)(7)(18))
= √(7² * 2² * 2² * 9)
= 2 * 2 * 3 * 7
= 84
Therefore, the area of the triangle with sides 25, 25, and 14 is 84 square units.