A triangle has an area of 15 cm^2 and a base of 5 cm. If a circle is drawn with a diameter equal to the length of the triangle's height, what is the area of the circle ?
a. 6 pi cm^2
b. 9 pi cm^2
c. 12 pi cm^2
d. 18 pi cm^2
e. 36 pi cm^2
please answer and explain
since a = bh/2, we have
h = 2a/b = 2*15/5 = 6
for a circle, a = pi r^2 = 9pi
To find the area of the circle, we first need to find the length of the triangle's height.
The area of a triangle is given by the formula: area = (base * height) / 2.
In this case, we are given the area as 15 cm^2 and the base as 5 cm. Substituting these values into the formula, we can solve for the height:
15 = (5 * height) / 2
30 = 5 * height
height = 30 / 5
height = 6 cm
Now that we know the height of the triangle is 6 cm, we can use this to find the diameter of the circle. The height of the triangle is equal to the diameter of the circle.
Thus, the diameter of the circle is 6 cm.
To find the area of the circle, we use the formula: area = pi * radius^2.
The radius of the circle is half the diameter. Therefore, the radius is equal to 6 / 2 = 3 cm.
Substituting this value into the formula, we can calculate the area of the circle:
area = pi * 3^2
area = pi * 9
area = 9 pi cm^2
Therefore, the area of the circle is 9 pi cm^2.
The correct answer is:
b. 9 pi cm^2