Arrow Area

Geometry Level 3

The lengths of particular sides of an arrow are given in the diagram above. If the total perimeter is 20, what is the enclosed area (to 3 decimal places)?

Note that the lengths of the slanted line segments are not explicitly given. The arrow is symmetrical with respect to its central vertical axis.


The answer is 15.165.

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2 solutions

Micah Wood
Nov 3, 2016

Since it is an arrow, we can assume that lengths of the slanted line segments are equal.

Now, sum of length of non-slanted line segments is 10 10 , so remaining should be 20 10 20-10 = 10 10 , hence slanted line segments are both length of 5 5 .

Now we can split this arrow into composite of triangle and rectangle. The area of rectangle is 3 × 2 = 6 3\times2 = 6

For area of triangle, we can use Heron's Formula . Result should be approximately 9.165 9.165

So the sum of these areas is 15.165 \boxed{15.165}

Denton Young
Jun 14, 2017

Length of slanted line segments = 5

Drop a perpendicular from the tip of the arrow to the base of the triangle. One side is 2, the hypotenuse is 5, so the height = 4.5825 and the triangle area is 9.165. Rectangle area = 6, so total area = 15.165

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