Given That The Area Of Triangle AQR is 32cm^2 such that AQ=8,AB=14,AR=10 and CR=7.2,calculate the area of triangle ABC.Plz! Answer My Question And Its A Homework!
To calculate the area of triangle ABC, we can use the formula for calculating the area of a triangle given its base and height. In this case, we need to find the height of triangle ABC.
Let's label the height of triangle ABC as h.
Since AQ and CR are parallel lines, we can use the similar triangles AQD and CRB to find the height of ABC.
Using similar triangles, we can set up the following proportion:
(AQ / AB) = (CR / CB)
Substituting the given values:
(8 / 14) = (7.2 / CB)
Cross-multiplying:
8 * CB = 14 * 7.2
CB = (14 * 7.2) / 8
CB = 12.6
Now that we have the height (CB), we can calculate the area of triangle ABC:
Area of triangle ABC = (1/2) * base * height
Area of triangle ABC = (1/2) * 14 * 12.6
Area of triangle ABC = 88.2 cm^2
Therefore, the area of triangle ABC is 88.2 square centimeters.
To find the area of triangle ABC, we need to use the concept of similar triangles.
First, let's draw a diagram to better understand the problem.
Triangle AQR and triangle ABC are similar triangles, which means their corresponding angles are equal, and their sides are proportional.
We are given that AQ = 8, AB = 14, and AR = 10. The length CR is not directly related to triangle ABC, so we won't need it for our calculations.
To find the area of triangle ABC, we need to know the length of BC.
Now, looking at triangle AQR, we can find the length of QR using the formula for the area of a triangle:
Area = 1/2 * base * height
The base of triangle AQR is AQ, which is 8 cm. Let's assume the height is h cm. So, we can write:
32 cm^2 = 1/2 * 8 cm * h cm
Simplifying this equation:
32 cm^2 = 4h cm^2
Dividing both sides by 4 cm^2:
8 cm = h
So, the height of triangle AQR is 8 cm.
Now, let's go back to triangle ABC. Since triangles AQR and ABC are similar, their corresponding sides are proportional.
Using the given values, we can set up the following ratio:
AQ/AB = QR/BC
Substituting the given values:
8/14 = 8/BC
Cross-multiplying:
8 * BC = 8 * 14
BC = 14 cm
Now we have the base length and the height of triangle ABC, which are AB = 14 cm and h = 8 cm, respectively.
To find the area of triangle ABC, we can apply the formula for the area of a triangle again:
Area = 1/2 * base * height
Area = 1/2 * 14 cm * 8 cm
Area = 56 cm^2
Therefore, the area of triangle ABC is 56 cm^2.