# Area of triangle

• Dec 15th 2009, 01:09 AM
rn5a
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
• Dec 15th 2009, 02:20 AM
earboth
Quote:

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 $\overline{ST} = height$
• Dec 15th 2009, 04:14 AM
jgv115
The problem is how to find the height of the whole triangle..
• Dec 15th 2009, 10:23 PM
earboth
Quote:

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

...

Quote:

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?
• Dec 15th 2009, 10:25 PM
jgv115