Shape and Space Solutions Week 2 Part 2.

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1. Playground with a Rectangular Area and a Semicircular Section

• Question: A playground consists of a rectangular area measuring 20 metres by 15 metres, with a semi-circular section at one end. The radius of the semicircle is 7.5 metres. Find the total area of the playground.

  
  

• Solution:

  1. Find the area of the rectangle:

     
     

     Area of Rectangle = Length × Width = 20 × 15 = 300 m²

     
     

  2. Find the area of the semicircle:

     
     

     Area of Semicircle = (π × Radius²) ÷ 2

     
     

     = (3.14 × 7.5 × 7.5) ÷ 2

     
     

     = (3.14 × 56.25) ÷ 2 = 88.31 m²

     
     

  3. Add both areas:

     
     

     Total Area = 300 + 88.31 = 388.31 m²

     
     

• Final Answer: The total area of the playground is 388.31 m².

  
  

2. Swimming Pool with Two Rectangular Sections

• Question: A swimming pool is in the shape of a large rectangle measuring 25 metres by 10 metres, with a smaller rectangular shallow end measuring 5 metres by 4 metres. Find the total area of the pool.

  
  

• Solution:

  1. Find the area of the large rectangle:

     
     

     Area of Large Rectangle = Length × Width = 25 × 10 = 250 m²

     
     

  2. Find the area of the smaller rectangle:

     
     

     Area of Small Rectangle = Length × Width = 5 × 4 = 20 m²

     
     

  3. Add both areas:

     
     

     Total Area = 250 + 20 = 270 m²

     
     

• Final Answer: The total area of the pool is 270 m².

  
  

3. Park with a Rectangular Path and a Triangular Flower Bed

• Question: A park has a walking path shaped like a large rectangle (30 metres by 20 metres) with a triangular flower bed at one corner. The base of the triangle is 10 metres, and the height is 8 metres. Calculate the combined area.

  
  

• Solution:

  1. Find the area of the rectangle:

     
     

     Area of Rectangle = Length × Width = 30 × 20 = 600 m²

     
     

  2. Find the area of the triangle:

     
     

     Area of Triangle = (Base × Height) ÷ 2

     
     

     = (10 × 8) ÷ 2 = 40 m²

     
     

  3. Add both areas:

     
     

     Total Area = 600 + 40 = 640 m²

     
     

• Final Answer: The combined area is 640 m².

  
  

4. Garden with a Rectangular Lawn and a Circular Flower Bed

• Question: A garden has a rectangular lawn measuring 15 metres by 10 metres, with a circular flower bed in the centre. The radius of the flower bed is 5 metres. Find the area of the lawn excluding the flower bed.

  
  

• Solution:

  1. Find the area of the rectangle:

     
     

     Area of Rectangle = Length × Width = 15 × 10 = 150 m²

     
     

  2. Find the area of the circle:

     
     

     Area of Circle = π × Radius² = 3.14 × (5 × 5) = 78.5 m²

     
     

  3. Subtract the area of the flower bed:

     
     

     Remaining Area = 150 − 78.5 = 71.5 m²

     
     

• Final Answer: The area of the lawn excluding the flower bed is 71.5 m².

  
  

5. Storage Shed with a Rectangular Base and a Triangular Roof

• Question: A storage shed is made of a rectangular base measuring 12 metres by 8 metres, with a triangular roof on top. The base of the triangle is 12 metres, and the height of the triangle is 4 metres. Find the total area of the shed's base and roof.

  
  

• Solution:

  1. Find the area of the rectangle (base):

     
     

     Area of Rectangle = Length × Width = 12 × 8 = 96 m²

     
     

  2. Find the area of the triangle (roof):

     
     

     Area of Triangle = (Base × Height) ÷ 2

     
     

     = (12 × 4) ÷ 2 = 24 m²

     
     

  3. Add both areas:

     
     

     Total Area = 96 + 24 = 120 m²

     
     

• Final Answer: The total area of the shed's base and roof is 120 m².

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