A rectangle measures 27 cm by 16 cm. One diagonal divides the rectangle into two triangles. Find the area of each triangle.

Answer

To find the area of each triangle formed by the diagonal of the rectangle, we can follow these steps:

### Step 1: Identify the dimensions of the rectangle
The rectangle has a length of 27 cm and a breadth of 16 cm.

### Step 2: Understand how the diagonal divides the rectangle
The diagonal of the rectangle divides it into two right-angled triangles. Let's label the rectangle as ABCD, where AB = 27 cm (length) and AD = 16 cm (breadth). The diagonal AC divides the rectangle into triangles ABC and ADC.

### Step 3: Use the formula for the area of a triangle
The area \( A \) of a triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
In our case, for triangle ABC:
- The base can be taken as AB (27 cm)
- The height can be taken as AD (16 cm)

### Step 4: Substitute the values into the formula
Substituting the values into the area formula:
\[ A = \frac{1}{2} \times 27 \times 16 \]

### Step 5: Calculate the area
First, calculate \( 27 \times 16 \):
\[ 27 \times 16 = 432 \]
Now, substitute this back into the area formula:
\[ A = \frac{1}{2} \times 432 = 216 \text{ cm}^2 \]

### Step 6: Conclusion
Since both triangles (ABC and ADC) are identical, the area of triangle ADC is also 216 cm². Thus, the area of each triangle is:
\[ \text{Area of each triangle} = 216 \text{ cm}^2 \]

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