A parallelogram cannot be a cross section of a triangular prism
2 answers:
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The area of the parallelogram whose vertices are (-4 , 9), (11 , 9), (5 , -1)
and (-10 ,-1) is 150 units²
Step-by-step explanation:
Let us revise some important facts:
1. Horizontal lines passe through points have same y-coordinates
2. The length of a horizontal segment is the difference between
the x-coordinates of its end-points
3. vertical lines passe through points have same x-coordinates
4. The length of a vertical segment is the difference between
the y-coordinates of its end-points
In the parallelogram whose vertices are
(-4 , 9), (11 , 9), (5 , -1) and (-10 ,-1)
∵ The vertices (-4 , 9) and (11 , 9) have same y-coordinates
∴ The side whose joining them is a horizontal side
∴ Its length = 11 - (-4) = 11 + 4 = 15 units
∵ The vertices (5 , -1) and (-10 , -1) have same y-coordinates
∴ The side whose joining them is a horizontal side
∴ Its length = 5 - (-10) = 5 + 10 = 15 units
∴ The two horizontal sides are parallel and equal
∵ The area of a parallelogram = ×
∵ The perpendicular distance between two parallel horizontal
sides is the difference between their y-coordinates
∵ The y-coordinate of the 1st horizontal side = 9
∵ The y-coordinate of the 2nd horizontal side = -1
∴ The vertical distance between the parallel sides = 9 - (-1) = 9 + 1
∴ The vertical distance between the parallel sides = 10 units
∵ = 15 units
∵ = 10 units
∴ The area of the parallelogram = 15 × 10 = 150 units²
The area of the parallelogram whose vertices are (-4 , 9), (11 , 9),
(5 , -1) and (-10 ,-1) is 150 units²
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