How do you find the area of a compound figure
2 answers:
Answer:
It depends on the figure.
Step-by-step explanation:
The compound figures we're generally concerned with are combinations of rectangles, triangles, circles or parts of circles, with or without cutouts of those shapes. The area is the sum of the areas of the component shapes, less the areas of any cutouts.
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Consider the attached examples:
7) This is half a circle together with two triangles. Or, the two triangles can be considered to be a rectangle with a triangular cutout.
The area is the sum of the areas of the semicircle and the rectangle, less the area of the triangular cutout.
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8) This can be considered as a square with a square cutout. The area is the difference between the area of the larger square and the area of the smaller one. Alternatively, one can find the area by finding the length of the centerline of the shaded area and multiplying that by the width of the shaded area.
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9) The area of this figure can be considered to be the total of the area of the bottom rectangle and the top triangle. Alternatively, one can cut the figure into two trapezoids (with a vertical line) and sum their areas.
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The line y = x and y = -x + 4 intersect when at the point (2, 2).
Expresing y = -x + 4 in terms of x, we have x = 4 - y.
Thus, the area of the region bounded by the <span>graphs of y = x, y = −x + 4, and y = 0 is given by
![\int\limits^2_0 {(y-(4-y))} \, dy = \int\limits^2_0 {(y-4+y)} \, dy \\ \\ = \int\limits^2_0 {(2y-4)} \, dy= \left[y^2-4y\right]_0^2 =|(2)^2-4(2)| \\ \\ =|4-8|=|-4|=4](https://tex.z-dn.net/?f=%20%5Cint%5Climits%5E2_0%20%7B%28y-%284-y%29%29%7D%20%5C%2C%20dy%20%3D%20%5Cint%5Climits%5E2_0%20%7B%28y-4%2By%29%7D%20%5C%2C%20dy%20%5C%5C%20%20%5C%5C%20%3D%20%5Cint%5Climits%5E2_0%20%7B%282y-4%29%7D%20%5C%2C%20dy%3D%20%5Cleft%5By%5E2-4y%5Cright%5D_0%5E2%20%3D%7C%282%29%5E2-4%282%29%7C%20%5C%5C%20%20%5C%5C%20%3D%7C4-8%7C%3D%7C-4%7C%3D4)
Therefore, the area bounded by the lines is 4 square units.
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Expresing y = -x + 4 in terms of x, we have x = 4 - y.
Thus, the area of the region bounded by the <span>graphs of y = x, y = −x + 4, and y = 0 is given by
Therefore, the area bounded by the lines is 4 square units.
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Relationship between distance and time is A. d = 0.12m
Step-by-step explanation:
For an object moving in uniform motion (=constant velocity), the relationship between distance covered and time taken is given by
where
d is the distance
v is the velocity
t is the time
Therefore, in order to find the relationship between distance and time, we have to find the velocity of the train.
This can be done by using the data of the table: in fact, the velocity is the ratio between the distance covered and the time taken to cover that distance.
Therefore, if we take for instance the last point of the table:
d = 2.4 miles (distance covered)
t = 20 minutes (time taken)
So the velocity is
And therefore, the relationship between distance and time is
(where m is the time in minutes)
Learn more about distance, time and velocity:
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