# Math Help - Area of triangle

1. ## Area of triangle

In the attached figure, ST=5cm & QR=9cm. The area of the larger triangle is 50 sq.cm. What is the area of the black region?

Thanks,

Ron

2. Originally Posted by rn5a
In the attached figure, ST=5cm & QR=9cm. The area of the larger triangle is 50 sq.cm. What is the area of the black region?

Thanks,

Ron

(area of the large triangle) - (area of triangle QRS)

The area of a triangle is calculated by:

$a_{\Delta} = \frac12 \cdot base \cdot height$

with $\overline{QR} = base$ and $\overline{ST} = height$

3. The problem is how to find the height of the whole triangle..

4. Originally Posted by rn5a
... The area of the larger triangle is 50 sq.cm. What is the area of the black region?

...
Originally Posted by jgv115
The problem is how to find the height of the whole triangle..
Honestly I don't understand why you want to know the height of the triangle QRP because you already know that the area of the this triangle is 50 cm².

But: Since you know that $\overline{QR} = 9\ cm$ you can use the value of the area and the length of the base to calculate the length of the height:

$50 =\frac12 \cdot 9 \cdot h~\implies~ h= \frac{100}9$

And now?

5. I should learn to read.

6. I thought you just subtract the area of the smaller traingle from the triangle of the whole to get 27.5 sq.cm?