Worksheet: Properties of Kites

In this worksheet, we will practice using the properties of kites, the Pythagorean theorem, and the polygon interior angles sum theorem to find measures in kites.

Q1:

If π‘Šπ‘‹π‘Œπ‘ is a kite, find π‘π‘Œ.

  • A13√2
  • B22
  • C17
  • D√314
  • E√74

Q2:

Given that 𝐴𝐡𝐢𝐷 is a kite, π‘šβˆ π΄=127∘, and π‘šβˆ π·=86∘, find π‘šβˆ πΆ.

Q3:

A kite has vertices at the points (2,0), (3,2), (4,0), and (3,βˆ’3).

Work out the perimeter of the kite. Give your solution to one decimal place.

Work out the area of the kite.

Q4:

Given that 𝐹𝐺𝐻𝐽 is a kite, where π‘šβˆ πΉπΊπ»=108∘ and π‘šβˆ πΉπ½π»=64∘, find π‘šβˆ πΊπΉπ½.

Q5:

Chloe wants to design a kite with two diagonals of lengths 46 cm and 78.2 cm. If she wants to join the midpoints of the kite’s sides using a string, how long should the string be?

Q6:

Complete the following: If 𝐴𝐡𝐢𝐷 is a quadrilateral in which 𝐴𝐡=𝐴𝐷 and 𝐡𝐢=𝐷𝐢, then ⃖⃗𝐴𝐢 is 𝐡𝐷.

  • Aequal to
  • Bthe perpendicular bisector of
  • Cparallel to
  • Dcongruent to

Q7:

If π‘Šπ‘‹π‘Œπ‘ is a kite, find π‘π‘Œ.

  • A26
  • B31
  • C24
  • D25
  • E√149

Q8:

If π‘Šπ‘‹π‘Œπ‘ is a kite, find π‘π‘Œ.

  • A√397
  • B24
  • C19
  • D√386
  • E√61

Q9:

Sophia wants to design a kite with two diagonals of lengths 74 cm and 162.8 cm. If she wants to join the midpoints of the kite’s sides using a string, how long should the string be?

Q10:

Given that 𝐴𝐡𝐢𝐷 is a kite, π‘šβˆ π΄=92∘, and π‘šβˆ π·=102∘, find π‘šβˆ πΆ.

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