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What is the area of the trapezoid? If necessary, round your answer to the nearest tenth.
1 answer:
The area of the trapezoid is calculated as 45.5 feet squared.
<h3></h3>What does Area of Trapezoid mean?
The entire area occupied by the sides of a trapezoid is its area. It's important to notice that if we know the lengths of all the sides, we can divide the trapezoid into smaller polygons, such as triangles and rectangles, calculate their areas, and then sum them all together to determine the area of the trapezoid.
<h3>The formula for Trapezoid Area:</h3>If the parallel sides of the trapezoid are known, along with their height, it is possible to determine their area. It is expressed as,
A=(a+b) h
where, A= the area of the trapezoid
h= height
'a' & 'b' = parallel side bases
<h3>Solution:</h3>a=5.5 feet , b= 8.5 feet & h=6.5 feet
A=(a+b)h
∴A=(5.5+8.5)*6.5
⇒A=(14)*6.5
⇒A=7*6.5
⇒A=45.5 feet squared
Therefore, the solution is (b) 45.5 feet squared.
Learn more about Trapezoid:
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Given:
The width at the base of parabolic tunnel is 7 m.
The ceiling 3 m from each end of the base there are light fixtures.
The height to light fixtures is 4 m.
To find:
Whether it is possible a trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel.
Solution:
The width at the base of tunnel is 7 m.
Let the graph of the parabola intersect the x-axis at x=0 and x=7. It means x and (x-7) are the factors of the height function.
The function of height is:
...(i)
Where, a is a constant.
The ceiling 3 m from each end of the base there are light fixtures and the height to light fixtures is 4 m. It means the graph of height function passes through the point (3,4).
Putting x=3 and h(x)=4 in (i), we get
Putting , we get
...(ii)
The center of the parabola is the midpoint of 0 and 7, i.e., 3.
The width of the truck is 4 m. If is passes through the center then the truck must m 2 m on the left side of the center and 2 m on the right side of the center.
2 m on the left side of the center is x=1.5.
A trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is possible if h(1.5) is greater than 2.8.
Putting x=1.5 in (ii), we get
It is clear that h(1.5)<2.8, therefore the trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is not possible.
