Question

The door mat which is in a hexagonal shape has the following
measures as given in the figure. Find its area.​

Answer 1

Answer:

The area of the hexagonal shaped door mat is 5600 cm²

Step-by-step explanation:

The figure given as the part of the question is attached.

As seen in the figure, the hexagonal doormat is symmetric about its diagonal 90 cm long.

This diagonal divides the area into two trapeziums of equal area

Thus, the area of the hexagon will be equal to the twice the area of one trapezium

The parallel sides of a trapezium are 70 cm and 90 cm long while the height of the trapezium is 35 cm

We know that area of trapezium = $\frac{1}{2} \times\text{sum of the parallel sides}\times \text{height}$

Thus, the area of one trapezium

= $\frac{1}{2}\times(70+90)\times35$ cm²

= $\frac{1}{2}\times160\times35$ cm²

Therefore, the area of the hexagon

= 2 × Area of the trapezium

= $2\times\frac{1}{2}\times160\times35$ cm²

= $160\times35$ cm²

= 5600 cm²

Answer 2

Step-by-step explanation:

The area of the hexagonal shaped door mat is 5600 cm²

Step-by-step explanation:

The figure given as the part of the question is attached.

As seen in the figure, the hexagonal doormat is symmetric about its diagonal 90 cm long.

This diagonal divides the area into two trapeziums of equal area

Thus, the area of the hexagon will be equal to the twice the area of one trapezium

The parallel sides of a trapezium are 70 cm and 90 cm long while the height of the trapezium is 35 cm

We know that area of trapezium = \frac{1}{2} \times\text{sum of the parallel sides}\times \text{height}

2

1

×sum of the parallel sides×height

Thus, the area of one trapezium

= \frac{1}{2}\times(70+90)\times35

2

1

×(70+90)×35 cm²

= \frac{1}{2}\times160\times35

2

1

×160×35 cm²

Therefore, the area of the hexagon

= 2 × Area of the trapezium

= 2\times\frac{1}{2}\times160\times352×

2

1

×160×35 cm²

= 160\times35160×35 cm²

= 5600 cm²