Question

1 Elon Musk has hired you to refabricate his private plane with carbon fibers. This is your chance for a lucrative career in the starship industry and to set your parents up for a very comfortable life and their golden years.
Break the blue parts of the plane into at least four shapes. For each shape, provide the following 1) shapes drawn on plane. 2) formula used, 3) all work calculated the area, 4) area of the shape, 5) sum of all blue Show all work on the graph below

Answer 1

The area of the blue parts of the plane comprises of four trapezoids,

from which each area can be calculated.

Response:

1) The drawings of the shapes are attached

$2) \hspace{0.3 cm}Area \ of \ a \ trapezoid \ A = \dfrac{a + b}{2} \times h$

3) The calculation for the area of each shape are;

• $Shape \ 1;\dfrac{2.2 + 1.6}{2} \times 4.6 = 8.74$

• $Shape \ 2;\dfrac{2.2 + 1.6}{2} \times 4.6 = 8.74$

• $Shape \ 3; \dfrac{0.9 + 1.7}{2} \times 1.6 = 2.08$

• $Shape \ 4; \dfrac{0.9 + 1.7}{2} \times 1.6 = 2.08$

4) Area of each shape is as follows;

• Shape 1; Area = 8.74 square units

• Shape 2; Area = 8.74 square units

• Shape 3; Area = 2.06 square units

• Shape 1; Area = 2.08 square units

5) Sum of all blue areas is 21.64 square units

Which method is used to break the blue parts?

The type of shape the blue parts break into are trapezoids

$Area \ of \ a \ trapezoid \ A = \mathbf{\dfrac{a + b}{2} \times h}$

Where;

a, and b are the lengths of the parallel sides;

h = The height of the trapezoid

The coordinates of the four shapes are;

• Shape 1 Coordinates; (0.6, 0), (-1.6, 0), (-0.4, 4.6), and (1.2, 4.6)

1) Please find attached the drawing of shape 1 created with MS Excel.

2) The formula for the area trapezoid formed by shape 1 is; $\dfrac{a + b}{2} \times h$

3) The area of the shape is, A = $\dfrac{2.2 + 1.6}{2} \times 4.6 = \mathbf{8.74}$

4) Area of shape 1 is 8.74 square units

• Shape 2 Coordinates: (0.6, 0), (-1.6, 0), (0.4, -4.6), and (1.2, -4.6)

1) The drawing of shape 2 created with MS Excel is attached

2) The formula for the area trapezoid formed by shape 2 is; $\dfrac{a + b}{2} \times h$

3) The area of the shape 2 is, A = $\dfrac{2.2 + 1.6}{2} \times 4.6 =\mathbf{ 8.74}$

4) Area of shape 2 is 8.74 square units

• Shape 3 Coordinates: (4, 0), (4.6, 1.6), (5.5, 1.6), (5.7, 0)

1) The drawing of shape 3 created with MS Excel is attached

2) The formula for the area trapezoid formed by shape 2 is; $\dfrac{a + b}{2} \times h$

3) The area of the shape 3 is, A = $\dfrac{0.9 + 1.7}{2} \times 1.6 = \mathbf{ 2.08}$

4) Area of shape 3 is 2.08 square units

Coordinates of shape 4; (4, 0), (4.6, -1.6), (5.5, -1.6), (5.7, 0)

1) The drawing of shape 4 created with MS Excel is attached

2) The formula for the area trapezoid formed by shape 2 is; $\dfrac{a + b}{2} \times h$

3) The area of the shape 4 is, A = $\dfrac{0.9 + 1.7}{2} \times 1.6 = \mathbf{2.08}$

4) Area of shape 4 is 2.08 square units

• 5) The sum of the area of the blue shapes = 2 × 8.74 + 2 × 2.08 = 21.64

Learn more about composite figures here:

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