Triangle ABC is a right triangle with right angle at C. CD is perpendicular to AB. BC=4 and CD=1. find the area of the triangle ABC.
2.07
To find the area of triangle ABC, we can use the formula for the area of a right triangle: (base * height) / 2.
In this case, BC is the base and CD is the height.
Given that BC = 4 and CD = 1, we can substitute these values into the formula.
Area = (base * height) / 2
= (4 * 1) / 2
= 4 / 2
= 2
Therefore, the area of triangle ABC is 2 square units.
To find the area of triangle ABC, we can use the formula for the area of a triangle:
Area = 1/2 * base * height
In this case, the base of the triangle is BC, which has a length of 4. The height of the triangle can be found by considering the length of CD, which is perpendicular to AB.
Since triangle ABC is a right triangle with a right angle at C, we can use the Pythagorean theorem to find the length of AB. The theorem states that the square of the hypotenuse (the longest side of the right triangle) is equal to the sum of the squares of the other two sides.
In this case, AB is the hypotenuse, BC is one of the other sides, and CD is the remaining side. Therefore, we have:
AB^2 = BC^2 + CD^2
Substituting the given values, we have:
AB^2 = 4^2 + 1^2
AB^2 = 16 + 1
AB^2 = 17
Taking the square root of both sides, we find:
AB = √17
So, the height of triangle ABC is √17 (since CD is the height and is perpendicular to AB).
Now, we can substitute the values into the formula for the area of a triangle:
Area = 1/2 * base * height
Area = 1/2 * 4 * √17
Area = 2 * √17
Therefore, the area of triangle ABC is 2√17.