Calculate the area of the shaded region shown in figure (iii) given below. All measurements are in meters.

The points are labelled as shown in the figure below:

Area of right angle △AEH = $\dfrac{1}{2}$ × base × height

= $\dfrac{1}{2}$ × AH × AE

= $\dfrac{1}{2}$ × 5 × 5

= 12.5 m².

Area of right angle △EBF = $\dfrac{1}{2}$ × base × height

= $\dfrac{1}{2}$ × BF × EB

= $\dfrac{1}{2}$ × 5 × 7

= 17.5 m².

Area of trapezium GDCF = $\dfrac{1}{2}$ × (sum of parallel sides) × distance between them

= $\dfrac{1}{2}$ × (GD + FC) × DC

= $\dfrac{1}{2}$ × (3 + 7) × 12

= 60 m².

Area of square ABCD = (side)² = (12)² = 144 m².

From figure,

Area of shaded region = Area of square ABCD - (Area of right angle △AEH + Area of right angle △EBF + Area of trapezium GDCF)

= 144 - (12.5 + 17.5 + 60)

= 144 - 90 = 54 m².

Hence, area of shaded region = 54 m².