Question

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
i think its 2

Answer 1

Answer:

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

Step-by-step explanation:

We are given that a polygon MNOPQR is shown. The top vertex on the left is labeled M, and the 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.

Firstly, we will draw a perpendicular line from point O which meets the line RQ at point T. Now, the polygon MNOPQR is divided into two rectangles MNTR and OPQT.

As we know that the area of the rectangle = $\text{Length of rectangle} \times \text{Breadth of rectangle}$

In the rectangle MNTR, the length (MN) = 5 units and the breadth (MR) = 3 units.

So, the area of the rectangle MNTR = $\text{Length (MN)} \times \text{Breadth (MR)}$

                                                            = $5 \times 3$  = 15 square units

Now, as we know that in rectangle MNTR, the side NT = 3 units and the side NO is labeled as 2 units. This means that the side OT = NT - NO = 3 units - 2 units = 1 unit

Similarly, the side QR is labeled as 7 units and the side RT is labeled as 5 units. This means that the side TQ = QR - RT = 7 - 5 = 2 units

Now, in the rectangle OPQT, the length (TQ) = 2 unit and the breadth (OT) = 2 units.

So, the area of the rectangle OPTQ = $\text{Length (TQ)} \times \text{Breadth (OT)}$

                                                            = $2 \times 1$  = 2 square units

Hence, the area of polygon MNOPQR = Area of a rectangle that is 15 square units + Area of a rectangle that is _2_ square units.