Calculate the Area of a Modified Rectangle: 6cm × 7cm with Erased Segment

The shape below consists of a rectangle from which the line segment BH has been erased.

AB=6
AC=7
EF=3
CD=12
BE=3

Calculate the area of the shape shaded orange.

Let's first calculate the area of triangle ABC:

$\frac{6\times7}{2}=\frac{42}{2}=21$

Since the shape before us is a rectangle, we can claim that:

AC=GD=7

Now let's calculate the area of triangle HGD:

$\frac{7\times3}{2}=\frac{21}{2}=10.5$

Let's draw an imaginary line between B and H to get square BEFH where each side equals 3 cm.

Let's calculate the area of BEFH:

$3\times3=9$

Let's calculate the area of rectangle ACDG:

$7\times12=84$

Now we can calculate the area of the brown shape by subtracting the other areas we found: