There is a pentagonal shaped part as shown in figure. For finding its area Jyoti and Rashida divided it in two different ways. Find the area in both ways and what do you observe?

Considering Jyoti’s Diagram first,

The pentagon given is divided into two equal trapeziums by Jyoti, whose height, h = 15/2 = 7.5 cm

Also, the parallel sides of each trapezium are of length 15cm and 30 cm.

As we know that,

Since the pentagon is made of two equal trapeziums, so the area of pentagon = twice the area of trapezium

⇒ Area of pentagon = 2 × area of trapezium

⇒ Req. area = 45 × 7.5 = 337.5 sq.cm

∴ area of pentagon as found by Jyoti is 337.5 sq. cm

Now, in case of Rashida,

She divided the pentagon to form a square and a triangle.

Side of square, a = 15 cm

Height of triangle, H = 30 – 15 = 15 cm

Area of square = a² = 15² = 225 sq.cm

⇒ Area of triangle = 112.5 sq.cm

Area of pentagon = Area of triangle + Area of square

⇒ 112.5 + 225

⇒ 337.5 sq.cm

∴ We see that, the area of pentagon found by both ways comes out to be same. Hence, It does not matter whichever way we divide a figure.