Question

Two straight lines are drawn onto a square to create four rectangles.

Work out the area of the rectangle marked A.
2 cm
W
3 cm
14 cm²
Q Zoom
A
Not drawn accurately

Answer 1

The area of rectangle A is found by dividing a square into four rectangles. With a base of 7 cm and a length (L) of 8 cm, the area is calculated as 56 cm² using the formula: Area = length × width.

1. The base of rectangle A is given as 7 cm.

`\[ (14)/(2) = 7 \, \text{cm} \]`

2. The sum of the length (L) and the width of the adjacent rectangle is given as 8 cm.

3 + 7 = 2 + L

3. Solve for the length (L):

L = 8 cm

4. Use the formula for the area of a rectangle (Area = length × width) to find the area of rectangle A:

`\[ \text{Area} = 7 * 8 = 56 \, \text{cm}^2 \]`

Therefore, the area of rectangle A is 56 cm², obtained through a step-by-step process involving geometric and algebraic reasoning.