`PQRS `is a rectangle in which side of `PQ = 24 cm`. and `QR= 16 cm`. T is a point on RS. What is the area (in cm.) of the triangle `PTQ`?

Options

A. 192
B. 162
C. 148
D. Cannot be determined

Answer

To find the area of triangle PTQ in rectangle PQRS, we will follow these steps:

### Step 1: Understand the dimensions of the rectangle.
- Given that PQ = 24 cm and QR = 16 cm, we can identify the lengths of the sides of rectangle PQRS.
- PQ is the length and QR is the width of the rectangle.

### Step 2: Identify the position of point T.
- Point T is located on side RS of the rectangle. Since RS is parallel to PQ, we can use the height from point P to line RS to find the area of triangle PTQ.

### Step 3: Determine the base and height of triangle PTQ.
- The base of triangle PTQ can be taken as PQ, which is 24 cm.
- The height of triangle PTQ is the distance from point P to line RS, which is equal to QR, or 16 cm.

### Step 4: Use the formula for the area of a triangle.
- The formula for the area of a triangle is:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]

### Step 5: Substitute the values into the formula.
- Here, the base = PQ = 24 cm and height = QR = 16 cm.
- Plugging in the values:
\[ \text{Area} = \frac{1}{2} \times 24 \times 16 \]

### Step 6: Calculate the area.
- First, calculate \( 24 \times 16 \):
\[ 24 \times 16 = 384 \]
- Now, divide by 2:
\[ \text{Area} = \frac{384}{2} = 192 \text{ cm}^2 \]

### Final Answer:
- The area of triangle PTQ is \( 192 \text{ cm}^2 \).

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