Worksheet: Trapezoid Midsegment Theorem

In this worksheet, we will practice finding unknown lengths in trapezoids using the trapezoid midsegment theorem.

Q1:

Suppose that 𝐴𝐡=128 and π‘‹π‘Œ=95. What is 𝐢𝐷?

Q2:

In the figure, 𝐿𝐻 is the midsegment of trapezoid 𝐹𝐺𝐽𝐾. What is the value of π‘₯?

Q3:

If 𝐡𝐴=24cm and 𝐷𝐢=26cm, find the length of 𝐾𝐹.

  • A𝐾𝐹=50cm
  • B𝐾𝐹=100cm
  • C𝐾𝐹=312cm
  • D𝐾𝐹=24.98cm
  • E𝐾𝐹=25cm

Q4:

Find the length of the middle base of a trapezoid whose parallel bases are 107 cm and 246 cm.

Q5:

In a trapezoid 𝐴𝐡𝐢𝐷 where 𝐴𝐷βˆ₯𝐡𝐢, the point 𝑋 is the midpoint of 𝐴𝐡, π‘Œ is the midpoint of 𝐷𝐢, and π‘‹π‘Œ=27cm. The area of the trapezoid is 513 cm2 and 𝐡𝐢=29cm.

Find the length of 𝐴𝐷 and the perpendicular distance between 𝐴𝐷 and 𝐡𝐢.

  • A𝐴𝐷=25cm, distance is 19 cm
  • B𝐴𝐷=83cm, distance is 17.7 cm
  • C𝐴𝐷=25cm, distance is 20.5 cm
  • D𝐴𝐷=83cm, distance is 19 cm
  • E𝐴𝐷=83cm, distance is 6.2 cm

Q6:

In the figure, 𝐿𝐻 is the midsegment of trapezoid 𝐹𝐺𝐽𝐾. What is the value of π‘₯?

Q7:

In the figure, 𝐿𝐻 is the midsegment of trapezoid 𝐹𝐺𝐽𝐾. What is the value of π‘₯?

Q8:

If 𝐡𝐴=10cm and 𝐷𝐢=12cm, find the length of 𝐾𝐹.

  • A𝐾𝐹=22cm
  • B𝐾𝐹=44cm
  • C𝐾𝐹=60cm
  • D𝐾𝐹=10.95cm
  • E𝐾𝐹=11cm

Q9:

If 𝐡𝐴=34cm and 𝐷𝐢=24cm, find the length of 𝐾𝐹.

  • A𝐾𝐹=58cm
  • B𝐾𝐹=116cm
  • C𝐾𝐹=408cm
  • D𝐾𝐹=28.57cm
  • E𝐾𝐹=29cm

Q10:

Find the length of the middle base of a trapezoid whose parallel bases are 14 cm and 46 cm.

Q11:

Find the length of the middle base of a trapezoid whose parallel bases are 27 cm and 54 cm.

Q12:

Suppose that 𝐴𝐡=168 and π‘‹π‘Œ=149. What is 𝐢𝐷?

Q13:

Suppose that 𝐴𝐡=196 and π‘‹π‘Œ=177.5. What is 𝐢𝐷?

Q14:

If the area of a trapezoid is 1,377 cm2, and its height is 51 cm, find the length of its middle base.

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