Triangular Area in a Rectangle

Geometry Level 2

$ABCD$ is a rectangle with $AB = 26$ , $BC= 11$ . $X$ , $Y$ and $Z$ are points on $AB$ , $BC$ and $CD$ , respectively, such that $AX = BY = CZ = 6$ . What is the area of triangle $XYZ$ ?

The answer is 68.

1 solution

Arron Kau Staff
May 13, 2014

Let $[PQRS]$ denote the area of figure $PQRS$ .

By rotational symmetry about the center of the rectangle, $[XBCZ] = [ZDAX]$ , hence is equal to $\frac {26 \times 11 } {2} = 143$ . We can also calculate that $[XBY] = \frac { (26-6)(6)}{2} = 60$ and $[YCZ] = \frac {(11-6)(6)} {2} = 15$ .

Thus, $[XYZ] = [XBCZ] - [XBY] - [YCZ] = 143 - 60 - 15 = 68$ .

Triangular Area in a Rectangle

The answer is 68.

1 solution

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