What is the volume of this shape?
1 answer:
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Answer:
2.2 metres squared
Step-by-step explanation:
We need to find the area of this trapezoid.
The area of a trapezoid is denoted by:
, where
and
are the parallel bases and h is the height
Here, we already know the lengths of the two bases; they are 0.9 metres and 2.3 metres. However, we need to find the length of the height.
Notice that one of the angles is marked 45 degrees. Let's draw a perpendicular line from top endpoint of the segment labelled 0.9 to the side labelled 2.3. We now have a 45-45-90 triangle with hypotenuse 2.0 metres. As one of such a triangle's properties, we can divide 2.0 by √2 to get the length of both legs:
2.0 ÷ √2 = √2 ≈ 1.414 ≈ 1.4
Thus, the height is h = 1.4 metres. Now plug all these values we know into the equation to find the area:
The answer is thus 2.2 metres squared.
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Answer:
Step-by-step explanation:
Since we are not given a midpoint, we use the Angle Addition Postulate:
156 = [x + 109] + [x + 53]
156 = 162 + 2x
-162 - 162
_______________
−6 = 2x
___ ___
2 2
−3 = x
[−3 + 53] + [−3 + 109] = 156
50 106
156 = 156 ☑
Therefore, is a genuine statement.
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Given:
The price of bananas can be determined by the equation P=0.25n, where P is the price and n is the number of bananas.
To find:
The constant of proportionality
Solution:
We have,
...(i)
where P is the price and n is the number of bananas.
Price P is directly proportional to the number of bananas. So,
...(ii)
Where, k is the constant of proportionality.
On comparing (i) and (ii), we get
Therefore, the constant of proportionality is 0.25.