The area of a trapezoid is 13 square meters. One base is 5 meters long and the other is 8 meters long. Find the height of the tr
1 answer:
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Please see the figure. We'll first work out half the area of the rounded triangle, half the unshaded part, then double it, then subtract it from the big square.
Half the area is the circular sector PTQ (with center P, arc TQ) minus the right triangle PUT.
A/2 = area(sector PTQ) - area(triangle PUT)
The triangle is half of equilateral triangle PQT, so a 30/60/90 right triangle so we know the sides are in ratio 1:√3:2 so
TU = (7/2)√3
area(PUT) = (1/2) (7/2)(7/2)√3 = (49/8)√3
area(sector PTQ) = (angle TQP / 360°) πr^2
We know angle TQP is 60° because TQP is equilateral. r=7.
area(sector PTQ) = (60°/360°) π (7²) = 49π/6
Putting it together,
A/2 = area(sector PTQ) - area(triangle PUT)
A = 2(49π/6 - (49/8)√3)
A = 49(π/3 - √3/4) square cm
I hate ruining a nice exact answer with an approximation, but they seem to be asking.
A ≈ 30.095057615914535
Check:
I'm not sure how to check it. I'd estimate it's about 25% bigger than equilateral triangle PQT with area (√3/4)7² ≈ 21.2, so around 27. 30 seems reasonable.
Now the real area we seek is the big square PQRS minus A, so
area = 7² - 30.095057615914535 = 18.904942384086 sq cm
They want square meters for some reason; we scale by (1/100)²
Answer: 0.00189 square meters
Answer:
113.04 cubic inches.
Step-by-step explanation:
We have been given that soft drinks are sold in aluminum cans that measure 6 inches in height and 2 inches in diameter.
To find the amount of drink contained in 6 cans, we will find the volume of 1 can using volume of cylinder formula.
, where,
r = Radius of cylinder,
h = Height of cylinder.
First of let us divide diameter of given cylinder by 2 to get the radius of our cylinder as diameter is 2 times the radius.
Upon substituting our given values in volume formula we will get,
Therefore, one can of soft drink contains 18.84 cubic inches of drink.
To find the amount of drink contained in 6 cans we will multiply volume of 1 can by 6.
Therefore, 6 cans of soft drink contain 113.04 cubic inches of drink.