A rectangular metal plate has dimensions of 45 cm by 30 cm. A right-angled triangular piece, featuring a base of 15 cm and a height of 10 cm, is removed from one of its corners. What is the area of the portion that remains?

The correct answer is 1275 cm².

To find the area of the portion of the metal plate that remains after cutting out a corner, we calculate the area of the original rectangular plate and subtract the area of the right-angled triangular piece that was removed.

Step 1: Calculate the total area of the original rectangular plate.

The area of a rectangle is calculated by multiplying its length by its width:

$\text{Area of rectangle}=\text{length}\times \text{width}$

Substituting the given dimensions (length = 45 cm, width = 30 cm):

$\text{Area of rectangle}=45\text{cm}\times 30\text{cm}=1350{\text{cm}}^2$

Step 2: Calculate the area of the right-angled triangular piece removed.

The area of a right-angled triangle is calculated using the formula:

$\text{Area of triangle}=\frac{1}{2}\times \text{base}\times \text{height}$

Substituting the given dimensions (base = 15 cm, height = 10 cm):

$\text{Area of triangle}=\frac{1}{2}\times 15\text{cm}\times 10\text{cm}=75{\text{cm}}^2$

Step 3: Calculate the area of the remaining portion.

Subtract the area of the removed triangle from the area of the original rectangle:

$\text{Remaining Area}=\text{Area of rectangle}-\text{Area of triangle}$

$\text{Remaining Area}=1350{\text{cm}}^2-75{\text{cm}}^2=1275{\text{cm}}^2$

Thus, the area of the portion that remains is 1275 cm².