ABCD is a rectangle measuring 60 cm by 50 cm P,Q,and R are the points on AB, AD , and BC, respectively, such that `AP = 40 cm, AQ = 20 cm, and BR = 40 cm. ` Find the area of the polygon QPBCD.

Answer

To find the area of the polygon QPBCD, we will follow these steps:

### Step 1: Calculate the area of rectangle ABCD
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]

For rectangle ABCD:
- Length = 60 cm
- Breadth = 50 cm

So, the area of rectangle ABCD is:
\[ \text{Area}_{ABCD} = 60 \, \text{cm} \times 50 \, \text{cm} = 3000 \, \text{cm}^2 \]

### Step 2: Identify the dimensions of triangle PAQ
In triangle PAQ:
- AP = 40 cm (base)
- AQ = 20 cm (height)

### Step 3: Calculate the area of triangle PAQ
The area of a triangle is given by the formula:
\[ \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \]

For triangle PAQ:
\[ \text{Area}_{PAQ} = \frac{1}{2} \times AP \times AQ = \frac{1}{2} \times 40 \, \text{cm} \times 20 \, \text{cm} \]

Calculating this gives:
\[ \text{Area}_{PAQ} = \frac{1}{2} \times 800 \, \text{cm}^2 = 400 \, \text{cm}^2 \]

### Step 4: Calculate the area of polygon QPBCD
To find the area of polygon QPBCD, we subtract the area of triangle PAQ from the area of rectangle ABCD:
\[ \text{Area}_{QPBCD} = \text{Area}_{ABCD} - \text{Area}_{PAQ} \]

Substituting the values we calculated:
\[ \text{Area}_{QPBCD} = 3000 \, \text{cm}^2 - 400 \, \text{cm}^2 = 2600 \, \text{cm}^2 \]

### Final Answer
The area of polygon QPBCD is:
\[ \text{Area}_{QPBCD} = 2600 \, \text{cm}^2 \]

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