Worksheet: Area of a Trapezoid

In this worksheet, we will practice finding the area of a trapezoid using a formula and applying it in finding the area in real life.

Q1:

Determine the perimeter and area of the accompanying figure.

  • Aperimeter =136mm, area =432mm
  • Bperimeter =112mm, area =336mm
  • Cperimeter =136mm, area =336mm
  • Dperimeter =112mm, area =432mm

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=12β„Ž(𝑏+𝑏). Use the formula to find the area of a trapezoid where β„Ž=6, 𝑏=14, and 𝑏=8.

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:

𝐴 𝐡 𝐢 𝐷 is a trapezium, and 𝐸𝑂𝐢𝐷 has three times the area of 𝐴𝐡𝑂𝐸 and 𝐸𝐴=4.5cm. What is π‘₯?

Q8:

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

Q9:

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

Q10:

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

  • AJames
  • BCharlotte

Q11:

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 58,206 mi2
  • B 28,511 mi2
  • C 57,023 mi2
  • D 47,411 mi2
  • E 46,228 mi2

Q12:

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

Q13:

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.

  • A A r e a c m = 1 1 , 7 6 0 , 0 0 0  , t o t a l c o s t = $ 4 , 7 0 4 . 0 0
  • B A r e a c m = 9 0 3 , 0 0 0  , t o t a l c o s t = $ 4 , 7 0 4 . 0 0
  • C A r e a c m = 9 , 0 3 0 , 0 0 0  , t o t a l c o s t = $ 3 , 6 1 2 . 0 0
  • D A r e a c m = 1 , 8 0 6 , 0 0 0  , t o t a l c o s t = $ 3 , 6 1 2 . 0 0
  • E A r e a c m = 1 8 , 0 6 0 , 0 0 0  , t o t a l c o s t = $ 7 , 2 2 4 . 0 0

Q14:

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

Q15:

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

Q16:

𝐴 𝐡 𝐢 𝐷 is a trapezium with 𝐴𝐷 parallel to 𝐡𝐢 and π‘šβˆ π΄=90∘. If 𝐡𝐢=9, 𝐴𝐷=18, and 𝐡𝐷=35, what is the area of the trapezium? Round to the nearest hundredth, if necessary.

Q17:

Work out the area of the shape.

Q18:

Find the area of this shape.

Q19:

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

Q20:

A right trapezoid is partitioned into 4 triangles by its diagonals as shown.

Which triangle has the larger area, the red one or the blue one?

  • Athe red one
  • Bthe blue one
  • CBoth are equal.
  • Dnot enough information

Q21:

Determine the perimeter and area of the accompanying figure.

  • Aperimeter =150mm, area =600mm
  • Bperimeter =110mm, area =450mm
  • Cperimeter =150mm, area =450mm
  • Dperimeter =110mm, area =600mm

Q22:

𝐴 𝐡 𝐢 𝐷 is a trapezium where 𝐴𝐷βˆ₯𝐡𝐢, 𝐴𝐷=22cm, and 𝐡𝐢=13cm. If the area of △𝐴𝐡𝐢 is 65 cm, what is the area of the trapezium?

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