Question

The figure below shows a shaded region and a non-shaded region. Angles in the figure that appear to be right angles are right angles.

Picture

What is the area, in square feet, of the shaded region?

What is the area, in square feet, of the non-shaded region?

Answer 1

Revising the formulas.

Let's divide the shape into 1 triangle and 2 rectangles.

• => Area of triangle = 1/2 x base x altitude
• => Area of rectangle = Length x Breadth

Finding the area of the triangle

• 1/2 x 10 x 3 = Area of triangle
• => 1 x 5 x 3 = Area of triangle
• => 15 feet² = Area of triangle

Finding the area of the SMALL rectangles

• (10 x 1) + (8 x 2) = Area of the small rectangles
• => 10 + 16 = Area of the small rectangles
• => 26 feet² = Area of the small rectangles

Finding the area of the figure

• 15 + 26 = Area of figure
• => 41 feet² = Area of figure

Finding the area of the BIG rectangle

• 8 x 16 = Area of BIG rectangle
• => 128 feet² = Area of BIG rectangle

Finding the area of the unshaded region

• 128 - 41 = Area of unshaded region
• => 87 feet² = Area of unshaded region

Answers:

• Part-1: 41 feet²
• Part-2: 87 feet²