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course Mth 151
9/91:16 pm
001. Areas
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Question: `q001. There are 11 questions and 7 summary questions in this assignment.
What is the area of a rectangle whose dimensions are 4 m by 3 meters.
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Your solution: A = L x W 4mx3m = 12 m2
confidence rating #$&*: 3
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Question: `q002. What is the area of a right triangle whose legs are 4.0 meters and 3.0 meters?
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Your solution: ½ b x h = A ½ * 4.0 * 3.0 = 6m2
confidence rating #$&*: 3
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Question: `q003. What is the area of a parallelogram whose base is 5.0 meters and whose altitude is 2.0 meters?
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Your solution: A = b * h 5 * 2 = 10m2
confidence rating #$&*: 3
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Question: `q004. What is the area of a triangle whose base is 5.0 cm and whose altitude is 2.0 cm?
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Your solution: ½ b * h = A ½ * 5.0 * 2.0 = 5cm2
confidence rating #$&*: 3
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Question: `q005. Sketch on a set of x-y axes the four-sided quadrilateral whose corners are at the points (3, 0), (3, 7), (9, 11) and (9, 0) (just plot these points, then connect them in order with straight lines).
What would you say is the width of this figure, as measured from left to right?
If the width is measured from left to right, why does it make sense to say that the figure has 'altitudes' of 7 and 11?
Do you agree that the figure appears to be a quadrilateral 'sitting' on the x axis, with 'altitudes' of 7 and 11?
We will call this figure a 'graph trapezoid'. You might recall from geometry that a trapezoid has two parallel sides, and that its altitude is the distance between those sides. The parallel sides are its bases. There is a standard formula for the area of a trapezoid, in terms of its altitude and its two bases. We are not going to apply this formula to our 'graph trapezoid', for reasons you will understand later in the course.
The 'graph trapezoid' you have sketched appears to be 'sitting' on the x axis. An object typically sits on its base. So we will think of its base as the side that runs along the x axis, the side it is 'sitting' on.
The 'graph trapezoid' appears to be 'higher' on one side than on the other. We often use the word 'altitude' for height. This 'graph trapezoid' therefore will be said to have two 'graph altitudes', 7 and 11.
What therefore would you say is the 'average graph altitude' of this trapezoid?
If you constructed a rectangle whose width is the same as that of this trapezoid, and whose length is the 'average graph altitude' of the trapezoid, what would be its area?
Do you think this area is more or less than the area of the 'graph trapezoid'?
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Your solution: I did sketch this and plot the trapezoid and I understand how to do so. What I do not understand is the graph altitude and in fact the graph trapezoid either.
confidence rating #$&*: 1
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Given Solution:
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Self-critique (if necessary): I have never been exposed to ‘graph trapezoid’ although I do know how to graph one. I just have never found the width, altitude, etc…
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Self-critique Rating:1
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