Niamh wants to extend her kitchen - Junior Cycle Mathematics - Question 1 - 2013

To find the area of the extension for each plan, we will calculate the area of the shaded regions separately.

Plan 1: The extension can be divided into two rectangles. The first rectangle has dimensions 4 m (width) and 6 m (height). Therefore, its area is:

$4 \times 6 = 24 \text{ m}^2$

Plan 2: The extension forms a triangle and a rectangle. The triangle has a base of 6 m and height of 2 m, and the rectangle has dimensions 6 m (width) and 3 m (height).

The area of the triangle is calculated as:

$\frac{1}{2}(6 \times 2) = 6 \text{ m}^2$

The area of the rectangle is:

$6 \times 3 = 18 \text{ m}^2$

Thus, the total area of Plan 2 is:

$6 + 18 = 15 \text{ m}^2$