GMAT prep question

[andreasonlinegr]

The correct answer is A = 12.5
But why is not B =14 -> base x height /2 = 7x4/2=14

any help much appreciated!

[Ian Stewart]

The correct answer is A = 12.5
But why is not B =14 -> base x height /2 = 7x4/2=14

Because the base is not equal to 7, and the height is not equal to 4. That would be the correct base and height if the coordinates of point Q were (0,4). But the length of the line from (7, 4) to (0, 3) is slightly greater than 7; you can use the Pythagorean Theorem to find that it's equal to sqrt(50) = 5*sqrt(2).

It's actually not straightforward to calculate the height of the triangle PQR directly (although it certainly is possible). I prefer to do these problems as follows:

-draw a rectangle with coordinates (0,0), (0,4), (7,4), (7,0).
-the area of the rectangle is 4*7 = 28.
-there are now three right angled triangles inside the rectangle but outside triangle PQR, with areas 7/2, 6 and 6.
-the area of triangle PQR is just the area of the rectangle minus the areas of the three right angled triangles: 28 - 7/2 - 6 - 6 = 12.5

[andreasonlinegr]

thats excellent. thank you very much. i wish i was that intelligent !!
thanks!!

[Sunny22uk]

You can also find the area by sing the formula
Area of triangle= Square root of s(s-a)(s-b)(s-c)
Where s= semi perimeter of the triangle i.e. sum of sides of traingle/2
Cheers