Worksheet: Area of a Trapezoid

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In this worksheet, we will practice finding the area of some trapezoidal objects in real life, like cities and yards.

Q1:

Determine the perimeter and area of the accompanying figure.

  • Aperimeter = 1 3 6 m m , area = 4 3 2 m m 2
  • Bperimeter = 1 1 2 m m , area = 3 3 6 m m 2
  • Cperimeter = 1 3 6 m m , area = 3 3 6 m m 2
  • Dperimeter = 1 1 2 m m , area = 4 3 2 m m 2

Q2:

The area of a trapezium is 1 900. If one of its parallel sides is 50 and its height is 50, what is the length of the other parallel side?

Q3:

A trapezium has area 1 760 and the distance between its parallel sides is 40. If one parallel side is 39, what is the other side?

Q4:

The area of a trapezoid is given by 𝐴 = 1 2 ℎ ( 𝑏 + 𝑏 ) 1 2 . Use the formula to find the area of a trapezoid where ℎ = 6 , 𝑏 = 1 4 1 , and 𝑏 = 8 2 .

Q5:

In a right trapezium, the parallel sides are 15 and 33, while their perpendicular is 44. What is its area?

Q6:

The given figure represents a trapezoidal wooden frame. Determine the surface area of its front side.

Q7:

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

Q8:

𝐴 𝐵 𝐶 𝐷 is a trapezium, and 𝐸 𝑂 𝐶 𝐷 has three times the area of 𝐴 𝐵 𝑂 𝐸 and 𝐸 𝐴 = 4 . 5 c m . What is 𝑥 ?

Q9:

The parallel sides of a trapezium have lengths 82 and 70. If the height is 100, what is its area?

Q10:

The area of a trapezium is 102, and the lengths of its parallel sides are 15 and 10. What is its height?

Q11:

Ramy said that he can draw several different trapezoids with a height of 2 and an area of 29. Sally disagrees and said that there is only one trapezoid with height 2 and area 29. Who is correct?

  • ARamy
  • BSally

Q12:

Arkansas has a shape that is similar to a trapezoid with bases of about 182 miles and 267 miles and a height of about 254 miles. Estimate the area of Arkansas.

  • A 4 7 4 1 1 mi2
  • B 4 6 2 2 8 mi2
  • C 5 8 2 0 6 mi2
  • D 5 7 0 2 3 mi2
  • E 2 8 5 1 1 mi2

Q13:

This trapezoid’s area is 30 000 yd2. What is its height?

Q14:

The given figure shows a backyard. Determine its area in square centimeters. If the backyard was priced for $4.00 per square meter, determine how much the backyard would cost.

  • AArea = 18 060 000 cm2. Total cost = $7 224.00
  • BArea = 903 000 cm2. Total cost = $4 704.00
  • CArea = 1 806 000 cm2. Total cost = $3 612.00
  • DArea = 9 030 000 cm2. Total cost = $3 612.00
  • EArea = 11 760 000 cm2. Total cost = $4 704.00

Q15:

Given that 𝑚 ∠ 𝐴 = 6 0 ∘ , find the area of 𝐴 𝐵 𝐶 𝐷 , to the nearest hundredth.

Q16:

A trapezoid of area 132 and base 20 has height 11. What is the length of the other base?

Q17:

𝐴 𝐵 𝐶 𝐷 is a trapezium where the lengths of its parallel bases 𝐴 𝐷 and 𝐵 𝐶 are 36 cm and 48 cm respectively. The length of the perpendicular drawn from 𝐷 to 𝐵 𝐶 is 35 cm. Find the area of 𝐴 𝐵 𝐶 𝐷 giving the answer to the nearest square centimetre.

Q18:

𝐴 𝐵 𝐶 𝐷 is a trapezium with 𝐴 𝐷 parallel to 𝐵 𝐶 and 𝑚 ∠ 𝐴 = 9 0 ∘ . If 𝐵 𝐶 = 9 , 𝐴 𝐷 = 1 8 , and 𝐵 𝐷 = 3 5 , what is the area of the trapezium? Round to the nearest hundredth, if necessary.

Q19:

Work out the area of the shape.

Q20:

In the trapezoid 𝐴 𝐵 𝐶 𝐷 , 𝑚 ∠ 𝐵 𝐴 𝐻 = 3 0 ∘ . Find the area of 𝐴 𝐵 𝐶 𝐷 in square feet. Round your answer to the nearest tenth.

Q21:

Find the area of this shape.

Q22:

Find, to the nearest integer, the area of this composite shape.

Q23:

A right Trapezium is partitioned into 4 triangles by its diagonals, as shown in the figure.

Which region has the larger area, red or blue?

  • Ablue
  • Bred
  • Cnot enough information
  • Dboth are equal

Q24:

Given that 𝑊 𝑋 𝑌 𝑍 is a trapezoid, 𝑍 𝑋 = 1 0 , and 𝑇 𝑌 = 7 , find 𝑊 𝑇 .

Q25:

Determine the perimeter and area of the accompanying figure.

  • Aperimeter = 1 5 0 m m , area = 6 0 0 m m 2
  • Bperimeter = 1 1 0 m m , area = 4 5 0 m m 2
  • Cperimeter = 1 5 0 m m , area = 4 5 0 m m 2
  • Dperimeter = 1 1 0 m m , area = 6 0 0 m m 2

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