LC)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 5 units. The side QR is labeled as 7 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 15 square units + Area of a rectangle that is ___ square units. (Input whole numbers only, such as 8.)

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barackodam barackodam · Answer 1 · 2022-07-14T20:55:55+02:00

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

From the information about the polygon MNOPQR, side MN is parallel to side RQ and also the side MR is parallel to side PQ

With a perpendicular line drawn from point O on the side RQ, which intersects with line RQ at point S.

We can then divide the polygon into two different rectangles

MNSR with A₁ as its area

OPQS with A₂ as its area

For rectangle MNSR, line MN is 5 units and line MR is 3 units

The formula for area of a rectangle is given as;

A₁ = (length)×(width)

Substitute the values

A₁ = 5 × 3

A₁ = 15 square units

For rectangle MNSR, line MN= line RS and line MR = line NS,

We have RS= 5 units and NS= 3 units

So, line SQ= RQ- RS = 7-5 = 2 units

Also, OS= NS - NO = 3- 2 = 1 unit

Let's substitute the values

A₂ = 2 × 1

A₂ = 2 square units

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

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