The outermost rectangle in the figure below is a square of 10 cm one side.
Find the area of the quadrangular shaded area.
Find the area of the quadrangular shaded area.
Answer
In other words, if you take out central rectangle from the square, the four rectangles will remain and the area of the shaded part is same to the area of four right triangle which are half of four rectangles respectively.
Therefore, the area of the shaded area is (10 × 10 - 2 × 3) / 2 + 2 × 3 = 53 cm2.
53 cm2
Solution
The area of the shaded portion excluding the area of the rectangle of 2cm × 3cm in the center, has become exactly half of the area excluding the area of the rectangle from that of the square.
In other words, if you take out central rectangle from the square, the four rectangles will remain and the area of the shaded part is same to the area of four right triangle which are half of four rectangles respectively.
Therefore, the area of the shaded area is (10 × 10 - 2 × 3) / 2 + 2 × 3 = 53 cm2.
