Let's start by calculating the area enclosed by the shape, which consists of a rectangle and a half-circle on the right side. I'll then outline how to find the perimeter as requested.

1. Area Calculation

Step 1: Area of the Rectangle

The rectangle has a length of 9 cm and a height of 6 cm.

$\text{Area of Rectangle} = \text{length} \times \text{height} = 9 \, \text{cm} \times 6 \, \text{cm} = 54 \, \text{cm}^2$

Step 2: Area of the Half-Circle

The diameter of the half-circle is the same as the height of the rectangle, which is 6 cm. This makes the radius $r$ of the half-circle 3 cm (since radius = diameter / 2).

Using $\pi = 3.14$: $\text{Area of Half-Circle} = \frac{1}{2} \pi r^2 = \frac{1}{2} \times 3.14 \times (3)^2 = \frac{1}{2} \times 3.14 \times 9 = 14.13 \, \text{cm}^2$

Step 3: Total Area

Now, we add the area of the rectangle and the half-circle.

$\text{Total Area} = 54 \, \text{cm}^2 + 14.13 \, \text{cm}^2 = 68.13 \, \text{cm}^2$

2. Perimeter Calculation

To find the perimeter, we need to calculate the lengths around the shape:

• The two vertical sides of the rectangle (6 cm each),
• The bottom side of the rectangle (9 cm),
• The semicircular arc (half the circumference of a circle with a 6 cm diameter).

Step 1: Perimeter of the Half-Circle

The circumference of a full circle with radius $r = 3$ cm is: $\text{Circumference} = 2 \pi r = 2 \times 3.14 \times 3 = 18.84 \, \text{cm}$ Since we only have half of the circle, the arc length of the half-circle is: $\text{Arc Length} = \frac{1}{2} \times 18.84 = 9.42 \, \text{cm}$

Step 2: Total Perimeter

Now, add up all the sides: $\text{Perimeter} = 6 + 6 + 9 + 9.42 = 30.42 \, \text{cm}$

Summary of Answers

• Total Area: $68.13 \, \text{cm}^2$
• Total Perimeter: $30.42 \, \text{cm}$

Would you like further details or have any questions?

Related Questions

1. How would the area change if the diameter of the half-circle was 8 cm instead?
2. What is the effect on the perimeter if the rectangle’s height is increased to 8 cm?
3. How would using a different value of $\pi$ (like 3.14159) affect the area?
4. If the rectangle were rotated 90 degrees, how would that impact the shape’s area or perimeter?
5. Can you find the perimeter of a full circle with a diameter of 6 cm?

Math Tip

When calculating areas of composite shapes, break down the shape into simpler parts, find each area separately, and then combine the results.