You can use the Pythagoras theorem to find the height of the triangle given and then by the height and the base of the triangle, you can find its area.
The area of the triangle ABC is 6 square units.
A right angled triangle is a triangle having one of its angle with measure of 90 degrees.
The slant side of that triangle is called Hypotenuse and it is the longest side in that triangle.
If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|2[/tex]
Refer to the diagram attached below.
Since we have right angle at angle A, and we have
|AC| = 4 units, |BC| = 5 units, let |AB| = [tex]x[/tex] units, then
[tex]|AC|^2 + |AB|^2 = |CB|^2\\4^2 + x^2 =5^2\\x ^2 = 25-16\\x = \sqrt{9} = 3 \text{\:(Positive root since x is length which is non negative quantity)}[/tex]
Area of a triangle is half of its base times height.
Since the line AC s perpendicular to AB, thus we can take base as AB and height as AC, then we have:
[tex]Area = \dfrac{1}{2} \times |AC| \times |AB| = \dfrac{1}{2} \times 4 \times 3 = 6 \: \rm unit^2[/tex]
Thus,
The area of the triangle ABC is 6 square units.
Learn more about right angled triangles here:
https://brainly.com/question/4456796
