the sum of the expanded angle is 180⇒
You start driving north for 9 miles, turn right, and drive east for another 40 miles. At the end of driving, what is your straig
1 answer:
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The area of the figure is 40 units. (rounded off from 39.998 units)
Step-by-step explanation:
1. Area of the figure = Area of Rectangle + Area of Parallelogram.
2. Naming points:
Let the rectangle consist of points A(-6,-1), B(-5,-5), C(3,-3) and D(2,1).
Let the parallelogram consist of points C(3,-3), D(2,1), E(2,7) and F(3,3).
3. Each coordinate has a point on the x-axis and a point on the y-axis. We shall refer to these points as x', x'' ,x''' and so on corresponding to the x-axis values of A, B, C and so on in that order till F. For the y-axis points, we will name them in the series of y', y'', y''' and so on.
In simple words, in A(-6,1), x' = -6; y' = -1
4. Formula for finding area:
Area of a rectangle = length (l) × width (w)
Area of a parallelogram = base (b) x height (h)
5. Finding area of the rectangle:
l = AD =
, i.e. AD =
, i.e. AD = √68 = 8.246 (rounded to 3 decimals) = l
Now, w = AB =
, i.e. AB =
, i.e. AB = √17 = 4.123 (rounded to 3 decimals) = w
Area of rectangle = l x w = 8.246 x 4.123 = 33.998 units.
6. Finding area of the parallelogram:
b = DE = 6 units (we can observe this from the graph, i.e. points from 1 to 7 on the y axis)
h = Height is the line drawn perpendicular to the base from point F, which as we can see is 1 unit long.
Hence, Area of parallelogram = b x h = 6 x 1 = 6 units.
7. Now, adding both, we can arrive at the final answer.
Area of the figure = Area of rectangle + Area of parallelogram,
i.e. 33.998 units + 6 units = 39.998 units. (can be rounded off to 40 units)
The vector ab has a magnitude of 20 units and is parallel to the
vector 4i + 3j. Hence, The vector AB is 16i + 12j.
<h3>How to find the vector?</h3>If we have given a vector v of initial point A and terminal point B
v = ai + bj
then the components form as;
AB = xi + yj
Here, xi and yj are the components of the vector.
Given;
The vector ab has a magnitude of 20 units and is parallel to the
vector 4i + 3j.
magnitude
Unit vector in direction of resultant = (4i + 3j) / 5
Vector of magnitude 20 unit in direction of the resultant
= 20 x (4i + 3j) / 5
= 4 x (4i + 3j)
= 16i + 12j
Hence, The vector AB is 16i + 12j.
Learn more about vectors;
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