Question

Math 13

A polygon is shown:

A polygon MNOPQR is shown. The top vertex on the left is labeled M, and rest of the vertices are labeled clockwise starting from the top left vertex labeled, M. The side MN is parallel to side QR. The side MR is parallel to side PQ. The side MN is labeled as 4 units. The side QR is labeled as 9 units. The side MR is labeled as 3 units, and the side NO is labeled as 2 units.

The area of polygon MNOPQR = Area of a rectangle that is 12 square units + Area of a rectangle that is square units. (Input only whole numbers, such as 8.)

Answer 1

The area of polygon MNOPQR = Area of a rectangle that is 15 square units + Area of a rectangle that is 2 square units.

In the given polygon MNOPQR, side MN is parallel to side RQ and the side MR is parallel to side PQ

We will draw a perpendicular line from point O on the side RQ, which will intersect RQ at point S. So, we can now divide the whole polygon into two different rectangles MNSR and OPQS with the areas as A₁ and A₂ respectively.

In rectangle MNSR, length(MN) = 5 units and width (MR) = 3 units

According to the formula for Area of rectangle,

A₁ = (length)×(width)

A₁ = (5 units)×(3 units)

A₁ = 15 square units

Now in rectangle MNSR, side MN= side RS and side MR = side NS,

so RS= 5 units and NS= 3 units

That means, SQ= RQ- RS = 7-5 = 2 units

and OS= NS - NO = 3- 2 = 1 unit

In rectangle OPQS, we have length(SQ) = 2 units and width(OS) = 1 unit

So, A₂ = (length)×(width)

A₂ = (2 units)×(1 unit)

A₂ = 2 square units

So, the area of polygon MNOPQR = (Area of a rectangle that is 15 square units + Area of a rectangle that is 2 square units)

Explanation: