what is the area of the isosceles triangle with side lengths of 17 meters,17 meters, and 30 meters

Question

 is it base height divided by two or what idk

Answer 1

The isosceles triangle can be divided into two right triangles where the common side is the height.  The area of each of those two triangles is:

      (1/2)(30/2)(SQRT(17^2-15^2)                 [using (1/2)bh]

      (1/2)(15)(8)

          60

So, the area of the isosceles triangles is 120 sq m.

Answer 2

Heron's Formula:

 

A = √(p(p - a)(p - b)(p - c)), where a, b, and c are the three sides and p is the semiperimeter, p = (a + b + c)/2

 

p = (17 + 17 + 30)/2

p = 32

 

A = √((32)(15)(15)(2))

A = √14400

A = 120

Answer 3

The area of a triangle is always (0.5)(base)(height). Always. The base is one side of the triangle. Pick a side, any side. The height is the distance from the base to the opposite corner.

 

Let's pick 30 for the base. The height is the distance from that side to the opposite corner. How do you calculate that? Draw a line from the base to the the opposite corner such that the line is perpendicular to the base. That creates two identical right triangles. Remember, a² + b² = c². In the case of your right triangles height² + 15² = 17². (How do you know that one of the sides is 15? Because it is an isosceles triangle, you know that the perpendicular line that you drew split the base exactly in half.) Moving on, height² + 225 = 289, so height² = 64, and height =8.

 

Now, back to the formula for area of a triangle: (0.5)(base)(height) Plugging in the numbers that we now have (0.5)(30)(8) = 120.

Answer 4

1. we will need to use some basic trigonometry for this one :)

2. first, we must divide the base by 2 so that we get a right triangle with a base of 15 and a hypotenuse of 17

3. now, let's call the angle that is adjacent to the base angle A

4. to find the angle, we do: cos(A) = adjacent/hypotenuse = 15/17, so A = cos^-1 (15/17) ≈ 28.072°

5. now, to find the height, we do: sin(28.072°) = height/17, so the height = 17*sin(28.072°) ≈ 8 meters

6. the area of a triangle = .5bh

7. therefore, .5*30*8 = 120 m²