Answer:
about 252.78 ft
Step-by-step explanation:
Define angle QMP as α. Then ...
MN = 60·sin(α)
NP = 60·cos(α)
area MPN = (1/2)(MN)(NP) = 1800sin(α)cos(α)
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PQ = 60tan(α)
area MPQ = (1/2)(MP)(PQ) = 1800tan(α)
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The ratio of areas is 2.5, so we have ...
1800tan(α) = 2.5·1800sin(α)cos(α)
1 = 2.5cos(α)² . . . . . . divide by 1800tan(α)
cos(α) = √0.4 . . . . . . solve for cos(α)
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Then the perimeter is ...
Perimeter = MN +NP +PQ +QM = 60sin(α) +60cos(α) +60tan(α) +60/cos(α)
= 60(sin(α) +cos(α) +tan(α) +sec(α))
= 60(0.774597 +0.632456 +1.224745 +1.581139)
= 60(4.212936) = 252.776
The perimeter of the trapezoid is about 252.776 feet.
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With perhaps a little more trouble, you can find the exact value to be ...
perimeter = (6√10)(7+√6+√15)
Answer:
square; perimeter 20 units; area 25 square units.
Step-by-step explanation:
As the attachment shows, each side of the polygon is the hypotenuse of a 3-4-5 right triangle, so has length 5 units. The perimeter is the sum of those lengths, 4×5 = 20; the area is the product of the lengths of adjacent sides, 5×5 = 25.
The figure is a square of side length 5 units.
The perimeter is 20 units; the area is 25 square units.
Answer:C=15
Step-by-step explanation:
Just do math
Answer:
<u>The correct answer is that the area of the regular octagon is 309 cm²</u>
Step-by-step explanation:
There are several formulas for calculating the area of a regular octagon. We will use this one for solving this question because it does not require additional information .
Area = (2 * s²)/tan 22,5°
s = 8 cm
Replacing with the real values, we have:
Area = (2 * 8²)/tan 22,5°
Area = 2 * 64/0.4142
Area = 128/0.4142
<u>Area = 309 cm² (Rounding to the nearest tenth)</u>
70 x 100 = 7,000
Therefore, 70 hundred is equal to 7 thousands.
