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Let's go through each problem and solve them step by step.

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### 1. **Find the area and circumference of the circles:**

   - **Circle 1 (radius = 10 m):**
     - **Area**: \( A = \pi r^2 = \pi \times 10^2 = 100\pi \) square meters.
     - **Circumference**: \( C = 2\pi r = 2\pi \times 10 = 20\pi \) meters.

   - **Circle 2 (radius = 8 m):**
     - **Area**: \( A = \pi r^2 = \pi \times 8^2 = 64\pi \) square meters.
     - **Circumference**: \( C = 2\pi r = 2\pi \times 8 = 16\pi \) meters.

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### 2. **Find the perimeter of the L-shaped figure:**

The L-shaped figure has the following dimensions:
- Vertical segments: 5 cm and 4 cm.
- Horizontal segments: 4 cm and 2 cm.

We need to sum all the sides:

\[ \text{Perimeter} = 5 + 4 + 4 + 2 = 15 \, \text{cm} \]

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### 3. **Find the surface area and volume of the rectangular prism:**

- Dimensions: \( 7 \, \text{cm} \times 5 \, \text{cm} \times 3 \, \text{cm} \).

   - **Surface area**:
     The formula for surface area \( A \) of a rectangular prism is:
     \[
     A = 2(lw + lh + wh)
     \]
     where \( l = 7 \, \text{cm}, w = 5 \, \text{cm}, h = 3 \, \text{cm} \).

     \[
     A = 2(7 \times 5 + 7 \times 3 + 5 \times 3) = 2(35 + 21 + 15) = 2 \times 71 = 142 \, \text{cm}^2
     \]

   - **Volume**:
     The volume \( V \) of a rectangular prism is:
     \[
     V = l \times w \times h = 7 \times 5 \times 3 = 105 \, \text{cm}^3
     \]

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### 4. **Calculate the volume of the triangular prism:**

   The triangular prism has a triangular base with dimensions:
   - Base = 6 cm,
   - Height of triangle = 5 cm,
   - Length of prism = 20 cm.

   The formula for the volume \( V \) of a triangular prism is:
   \[
   V = \frac{1}{2} \times \text{base of triangle} \times \text{height of triangle} \times \text{length}
   \]
   \[
   V = \frac{1}{2} \times 6 \times 5 \times 20 = 300 \, \text{cm}^3
   \]

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### 5. **Find the area of the shape:**

This problem involves a composite shape made up of two rectangles. The dimensions given are:
   - Large rectangle: \( 11 \, \text{cm} \times 14 \, \text{cm} \),
   - Small rectangle: \( 6 \, \text{cm} \times 4 \, \text{cm} \).

   The total area is:
   \[
   A = (11 \times 14) - (6 \times 4) = 154 - 24 = 130 \, \text{cm}^2
   \]

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### 6. **Find \( x \) in the triangle:**

The given triangle has angles:
   - \( 40^\circ \),
   - \( 70^\circ \), and
   - \( x^\circ \).

   Since the sum of angles in a triangle is \( 180^\circ \):
   \[
   x = 180^\circ - (40^\circ + 70^\circ) = 180^\circ - 110^\circ = 70^\circ
   \]

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Would you like more details or have any questions about these solutions?

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Here are 5 related questions to explore further:

1. How do you calculate the area of a sector of a circle?
2. Can you find the volume of a cone given its height and radius?
3. How would you calculate the surface area of a sphere?
4. What is the difference between perimeter and circumference?
5. How do you find the height of a triangle if only the base and area are known?

**Tip:** Always keep in mind the correct units when solving geometry problems. For areas, it's squared units, and for volume, it's cubed units!

Find the area and circumference of two circles, the perimeter of an L-shaped figure, the surface area and volume of a rectangular prism, the volume of a triangular prism, the area of a composite shape, and the missing angle x in a triangle.

Learn how to solve various geometry problems involving circles, L-shaped figures, rectangular prisms, and triangles. This includes calculating area, circumference, perimeter, surface area, volume, and finding missing angles. Suitable for Grades 6-9.

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