Worksheet: Isosceles Trapezoids

In this worksheet, we will practice identifying an isosceles trapezoid and using its properties to solve word problems.

Q1:

Choose the option that makes this sentence true: A trapezoid have exactly one pair of congruent sides.

  • A will always
  • B can never
  • C can

Q2:

How many trapeziums can you count?

Q3:

The figure shows an isosceles trapezoid. Given that 𝐹 𝐾 = 9 and 𝐽 𝐺 = 2 6 , find 𝐾 𝐻 .

Q4:

Which statement is true for the given trapezoid?

  • A The trapezoid has two pairs of parallel sides.
  • B The trapezoid has two right angles.
  • C The trapezoid has three obtuse angles.
  • D The trapezoid has two acute angles.
  • E The trapezoid has two pairs of perpendicular sides.

Q5:

The speaker shown is an isosceles trapezoid. If 𝑚 𝐹 𝐽 𝐻 = 8 2 , find 𝑚 𝐹 𝐺 𝐻 .

Q6:

Given that 𝐽 𝐾 𝐿 𝑀 is a trapezoid and 𝑚 𝑀 = 6 8 , find 𝑚 𝐾 .

Q7:

Given that 𝐴 𝐵 𝐶 𝐷 is a trapezoid and 𝑚 𝐵 𝐶 𝐷 = 1 0 1 , find 𝑚 𝐷 .

Q8:

A frame is to be constructed in the shape of a regular trapezoid with a perimeter of 50 inches and a height of 8 inches, where both of the nonparallel sides have a length of 10 inches. Work out the lengths of the two parallel sides.

  • A 5 and 25 inches
  • B 15 and 15 inches
  • C 20 and 20 inches
  • D 9 and 21 inches
  • E 12 and 28 inches

Q9:

Given that Engy is cutting a piece of fabric, where the top of the piece measures 2 ft, the bottom measures 3 ft, and each side measures 4 ft, determine the shape she is cutting the fabric.

  • Aa triangle
  • Ba rectangle
  • Ca parallelogram
  • Da trapezoid
  • Ea cube

Q10:

𝐴 𝐵 𝐶 𝐷 is an isosceles trapezium where 𝐴 𝐵 = 𝐴 𝐷 = 𝐷 𝐶 = 8 c m and 𝐵 𝐶 = 1 6 c m . Find the area giving the answer to two decimal places.

Q11:

Find the area of an isosceles trapezium 𝐴 𝐵 𝐶 𝐷 , given 𝐴 𝐵 = 𝐴 𝐷 = 𝐷 𝐶 = 3 c m and 𝐵 𝐶 = 5 c m . Give the answer to one decimal place.

Q12:

An isosceles trapezium of area 74 is divided into two symmetrical pieces by its line of symmetry. What is the area of each piece?

  • A18.5
  • B74
  • C55.5
  • D37
  • E148

Q13:

If 𝐸 𝐵 𝑀 𝐿 is an isosceles trapezium, then which of the following is true?

  • A 𝐿 𝐸 = 𝐿 𝐵
  • B 𝑀 𝐸 = 𝑀 𝐵
  • C 𝐿 𝑀 = 𝐸 𝐵
  • D 𝑀 𝐸 = 𝐿 𝐵
  • E 𝐿 𝐺 = 𝐺 𝐵

Q14:

The figure shows an isosceles trapezoid. Given that 𝐹 𝐾 = 8 and 𝐽 𝐺 = 2 7 , find 𝐾 𝐻 .

Q15:

The figure shows an isosceles trapezoid. Given that 𝐹 𝐾 = 8 and 𝐽 𝐺 = 2 3 , find 𝐾 𝐻 .

Q16:

Given that 𝐴 𝐵 𝐶 𝐷 is a trapezoid and 𝑚 𝐵 𝐶 𝐷 = 1 2 2 , find 𝑚 𝐷 .

Q17:

Given that 𝐽 𝐾 𝐿 𝑀 is a trapezoid and 𝑚 𝑀 = 6 3 , find 𝑚 𝐾 .

Q18:

The speaker shown is an isosceles trapezoid. If 𝑚 𝐹 𝐽 𝐻 = 7 5 , find 𝑚 𝐹 𝐺 𝐻 .

Q19:

The speaker shown is an isosceles trapezoid. If 𝑚 𝐹 𝐽 𝐻 = 6 8 , find 𝑚 𝐹 𝐺 𝐻 .

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