Geometric Modeling Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
A garden is modelled as a rectangle 2020 m long and 88 m wide. Calculate the area to be planted and the length of fencing needed.

Solution

  1. 1
    Step 1: Model the garden as a rectangle with l=20l = 20 m and w=8w = 8 m.
  2. 2
    Step 2: Area =l×w=20×8=160= l \times w = 20 \times 8 = 160 m2^2.
  3. 3
    Step 3: Perimeter (fencing) =2(l+w)=2(20+8)=2(28)=56= 2(l + w) = 2(20 + 8) = 2(28) = 56 m.

Answer

Area =160= 160 m2^2; fencing needed =56= 56 m.
Geometric modelling means choosing a shape (here a rectangle) to represent a real-world object. Once modelled, standard formulas give useful measurements. The accuracy of the model depends on how well a rectangle approximates the actual garden.

About Geometric Modeling

Using geometric shapes and their relationships to represent, approximate, and analyze real-world objects and situations.

Learn more about Geometric Modeling →

More Geometric Modeling Examples

Example 2 medium

A can of soup is modelled as a cylinder. The can is [formula] cm tall and [formula] cm in diameter.

Example 3 easy

A triangular warning sign has a base of [formula] cm and height of [formula] cm. What area of reflec

Example 4 hard

A swimming pool has a rectangular flat bottom ([formula]) with a semicircular end on each short side

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