Answer:
4.06 cm^2
Explanation:
If you draw a line from the top vertex to intersect the base (which is 5.8 cm) at 90 degrees, the line is called the height. You need to calculate the height to determine the area.
So the triangle's height will divide the triangles into 2 smaller right triangles.
For the left right triangle, 2.5 will be hypotenuse
=> 2.5^2 = (height)^2 + (base1)^2
=> (height)^2 = 6.25 - (base1)^2
For the right right triangle, 4 will be hypotenuse
=> 4^2 = (height)^2 + (base2)^2
=> (height)^2 = 16 - (base2)^2
So
6.25 - (base1)^2 = 16 - (base2)^2
We have base1 + base2 = 5.8 => base1 = 5.8 - base2
Substitute
6.25 - (5.8 - base2)^2 = 16 - (base2)^2
6.25 - (33.64 - 11.6base2 + base2^2 = 16 - base2^2
base2^2 - base2^2 + 11.6base2 = 16 + 33.6 - 6.25
11.6base2 = 43.35
base2 = 43.35/11.6 = 3.74
since (height)^2 = 16 - (base2)^2
(height)^2 = 16 - (3.74)^2
height^2 = 2.0124
height = 1.42
so area = 1/2hb = 1/2(1.4)(5.8) = 4.06 cm^2