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
[tex]2) \hspace{0.3 cm}Area \ of \ a \ trapezoid \ A = \dfrac{a + b}{2} \times h[/tex]
3) The calculation for the area of each shape are;
- [tex]Shape \ 1;\dfrac{2.2 + 1.6}{2} \times 4.6 = 8.74[/tex]
- [tex]Shape \ 2;\dfrac{2.2 + 1.6}{2} \times 4.6 = 8.74[/tex]
- [tex]Shape \ 3; \dfrac{0.9 + 1.7}{2} \times 1.6 = 2.08[/tex]
- [tex]Shape \ 4; \dfrac{0.9 + 1.7}{2} \times 1.6 = 2.08[/tex]
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
[tex]Area \ of \ a \ trapezoid \ A = \mathbf{\dfrac{a + b}{2} \times h}[/tex]
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; [tex]\dfrac{a + b}{2} \times h[/tex]
3) The area of the shape is, A = [tex]\dfrac{2.2 + 1.6}{2} \times 4.6 = \mathbf{8.74}[/tex]
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; [tex]\dfrac{a + b}{2} \times h[/tex]
3) The area of the shape 2 is, A = [tex]\dfrac{2.2 + 1.6}{2} \times 4.6 =\mathbf{ 8.74}[/tex]
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; [tex]\dfrac{a + b}{2} \times h[/tex]
3) The area of the shape 3 is, A = [tex]\dfrac{0.9 + 1.7}{2} \times 1.6 = \mathbf{ 2.08}[/tex]
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; [tex]\dfrac{a + b}{2} \times h[/tex]
3) The area of the shape 4 is, A = [tex]\dfrac{0.9 + 1.7}{2} \times 1.6 = \mathbf{2.08}[/tex]
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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