Perimeter of a kite?

Hey, could anyone here please find the perimeter of this kite? I'm kind of stuck. 

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  • 2 months ago
    Favourite answer

    A kite has bilateral symmetry, so the two short segments on the perimeter are the same, and the two long segments are the same.

    The diagonals cross at right angles forming 2 pairs of right triangles.

    Looking at the small triangles on the left, they have legs of 7 and 24. Use the Pythagorean Theorem (or your knowledge of Pythagorean Triples) to find the hypotenuse.

    7² + 24² = c²

    49 + 576 = c²

    c² = 625

    c = √625

    c = 25

    So the two short segments on the perimeter are 25 and 25. The two long segments would be 92.179 and 92.179, as marked. 

    At this point you can stop and add up the 4 sides and be done.

    P = 25 + 25 + 92.179 + 92.179

    P = 234.358 

    However, if they hadn't given you the measurement of the long segments, you could have still figured it out from the two large right triangles on the right.

    The full diagonal is 96, so the long leg would be 96-7 = 89. And the short leg is 24.

    24² + 89² = d²

    576 + 7921 = d²

    d² = 8497

    d = √8497

    d ≈ 92.179

    Add them up as before:

    P = 25 + 25 + 92.179 + 92.179

    P = 234.358

    Answer:

    ~234.358

    • tomlinson2 months agoReport

      thank you so much! that was even more than i needed! i really appreciate it

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  • Laurie
    Lv 7
    2 months ago

    Add the hypotenuses of the four right triangles together. I’m unsure whether the “24” pertains to the entire vertical line, or just half. The small triangles have sides of 7 and 24 (or 12) ; the larger triangles have sides of (96 - 7) and 24 (or 12).

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