Question

Find the area of the shaded region.

Answer 1

The region is made up of

• a right triangle with short leg 10 m and hypotenuse 26 m

• a parallelogram with sides 40 m and 26 m (the 26-m side corresponds to the aforementioned hypotenuse)

• another triangle with two known legs of length 20 m and 26 m

Find the height of the right triangle using the Pythagorean theorem. If the height is h, then

(10 m)² + h² = (26 m)²   ⇒   h² = 576 m²   ⇒   h = 24 m

This height is common to all three shapes.

Now find the area of each shape.

• right triangle:

1/2 × (10 m) × (24 m) = 120 m²

• parallelogram:

(40 m) × (24 m) = 960 m²

• other triangle:

• 1/2 × (20 m) × (24 m) = 240 m²

Then the total area of the shaded region is 1320 m².