Question

irregular shapes.

Explanation:

Assuming the problem is to find the area of this irregular shape (composed of a rectangle and two semicircles, which make a full circle), we can solve it as follows:

Step1: Identify the components

The shape consists of a rectangle with length \( l = 21 \, \text{cm} \) and width equal to the diameter of the circle (since the radius of the semicircles is \( 7 \, \text{cm} \), the diameter \( d = 2\times7 = 14 \, \text{cm} \)), and a circle with radius \( r = 7 \, \text{cm} \) (formed by the two semicircles).

Step2: Calculate the area of the rectangle

The area of a rectangle is given by \( A_{\text{rectangle}} = l \times w \). Here, \( l = 21 \, \text{cm} \) and \( w = 14 \, \text{cm} \) (diameter of the circle). So,
\( A_{\text{rectangle}} = 21 \times 14 = 294 \, \text{cm}^2 \)

Step3: Calculate the area of the circle

The area of a circle is given by \( A_{\text{circle}} = \pi r^2 \). Here, \( r = 7 \, \text{cm} \), so,
\( A_{\text{circle}} = \pi \times 7^2 = 49\pi \approx 49\times3.14 = 153.86 \, \text{cm}^2 \)

Step4: Calculate the total area

The total area of the irregular shape is the sum of the area of the rectangle and the area of the circle.
\( A_{\text{total}} = A_{\text{rectangle}} + A_{\text{circle}} = 294 + 153.86 = 447.86 \, \text{cm}^2 \) (or using \( \pi = \frac{22}{7} \), \( A_{\text{circle}} = \frac{22}{7} \times 49 = 154 \, \text{cm}^2 \), so \( A_{\text{total}} = 294 + 154 = 448 \, \text{cm}^2 \))

Answer:

The area of the irregular shape is approximately \( \boldsymbol{447.86 \, \text{cm}^2} \) (or \( \boldsymbol{448 \, \text{cm}^2} \) if using \( \pi = \frac{22}{7} \)).