Quadrilateral Worksheets - Free Printable

Let’s solve each problem one by one. We’ll use the fact that in a parallelogram, opposite sides are equal, and in some cases (like rectangles or rhombuses), we might have extra properties — but here, most look like parallelograms unless marked otherwise.

We’ll go row by row, left to right.

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Problem 1:
Sides:
Top = 3x + 5
Bottom = 4x - 2
Left = y + 3
Right = 2y - 1

Since it’s a parallelogram, top = bottom and left = right.

Set up equations:

→ 3x + 5 = 4x - 2
Subtract 3x from both sides:
5 = x - 2
Add 2 to both sides:
x = 7

Now plug x back in to find side lengths:
Top = 3(7) + 5 = 21 + 5 = 26
Bottom = 4(7) - 2 = 28 - 2 = 26 → matches!

Now for y:
y + 3 = 2y - 1
Subtract y from both sides:
3 = y - 1
Add 1:
y = 4

Left = 4 + 3 = 7
Right = 2(4) - 1 = 8 - 1 = 7 → matches!

✔ So for Problem 1:
x = 7, y = 4
Side lengths: Top/Bottom = 26, Left/Right = 7

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Problem 2:
Sides:
Top = 2x + 1
Bottom = 3x - 4
Left = y + 2
Right = 2y - 3

Again, parallelogram → opposite sides equal.

So:

2x + 1 = 3x - 4
Subtract 2x:
1 = x - 4
Add 4:
x = 5

Check:
Top = 2(5)+1 = 11
Bottom = 3(5)-4 = 15-4=11 → good.

Now y:

y + 2 = 2y - 3
Subtract y:
2 = y - 3
Add 3:
y = 5

Left = 5+2=7
Right = 2(5)-3=10-3=7 → good.

✔ Problem 2:
x = 5, y = 5
Side lengths: Top/Bottom = 11, Left/Right = 7

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Problem 3:
This is NOT a parallelogram — it has a right angle mark and different side labels. Looks like a trapezoid? But wait — actually, looking at the diagram description (even though we can’t see image, based on standard problems), this may be a rectangle or just a quadrilateral with given expressions.

Wait — let me re-read the user's input. The original says “Sides of a Quadrilateral” and asks to solve for x and y and find indicated side lengths.

In problem 3, sides are labeled:

Top: 2x + 3
Right: y + 1
Bottom: 3x - 2
Left: 2y - 3

But there’s a right angle symbol — so maybe it’s a rectangle? In a rectangle, opposite sides are equal AND all angles are 90°.

Assume it’s a rectangle → then top = bottom and left = right.

So:

2x + 3 = 3x - 2
Subtract 2x:
3 = x - 2
Add 2:
x = 5

Then top = 2(5)+3=13, bottom=3(5)-2=13 → good.

Now left = right:

2y - 3 = y + 1
Subtract y:
y - 3 = 1
Add 3:
y = 4

Left = 2(4)-3=5, Right=4+1=5 → good.

✔ Problem 3:
x = 5, y = 4
Side lengths: Top/Bottom = 13, Left/Right = 5

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Problem 4:
Sides:
Top: 3x + 1
Bottom: 4x - 3
Left: y + 4
Right: 2y - 2

Parallelogram → opposite sides equal.

So:

3x + 1 = 4x - 3
Subtract 3x:
1 = x - 3
Add 3:
x = 4

Top = 3(4)+1=13, Bottom=4(4)-3=13 → good.

Now y:

y + 4 = 2y - 2
Subtract y:
4 = y - 2
Add 2:
y = 6

Left = 6+4=10, Right=2(6)-2=10 → good.

✔ Problem 4:
x = 4, y = 6
Side lengths: Top/Bottom = 13, Left/Right = 10

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Problem 5:
Sides:
Top: 2x + 5
Bottom: 3x - 1
Left: y + 3
Right: 2y - 4

Parallelogram → set opposites equal.

2x + 5 = 3x - 1
Subtract 2x:
5 = x - 1
Add 1:
x = 6

Top = 2(6)+5=17, Bottom=3(6)-1=17 → good.

y + 3 = 2y - 4
Subtract y:
3 = y - 4
Add 4:
y = 7

Left = 7+3=10, Right=2(7)-4=10 → good.

✔ Problem 5:
x = 6, y = 7
Side lengths: Top/Bottom = 17, Left/Right = 10

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Problem 6:
Sides:
Top: 4x - 2
Bottom: 5x - 6
Left: y + 1
Right: 2y - 3

Parallelogram → opposites equal.

4x - 2 = 5x - 6
Subtract 4x:
-2 = x - 6
Add 6:
x = 4

Top = 4(4)-2=14, Bottom=5(4)-6=14 → good.

y + 1 = 2y - 3
Subtract y:
1 = y - 3
Add 3:
y = 4

Left = 4+1=5, Right=2(4)-3=5 → good.

✔ Problem 6:
x = 4, y = 4
Side lengths: Top/Bottom = 14, Left/Right = 5

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Problem 7:
Sides:
Top: 3x + 2
Bottom: 4x - 3
Left: y + 5
Right: 2y - 1

Parallelogram → opposites equal.

3x + 2 = 4x - 3
Subtract 3x:
2 = x - 3
Add 3:
x = 5

Top = 3(5)+2=17, Bottom=4(5)-3=17 → good.

y + 5 = 2y - 1
Subtract y:
5 = y - 1
Add 1:
y = 6

Left = 6+5=11, Right=2(6)-1=11 → good.

✔ Problem 7:
x = 5, y = 6
Side lengths: Top/Bottom = 17, Left/Right = 11

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Problem 8:
Sides:
Top: 2x + 4
Bottom: 3x - 1
Left: y + 2
Right: 2y - 3

Parallelogram → opposites equal.

2x + 4 = 3x - 1
Subtract 2x:
4 = x - 1
Add 1:
x = 5

Top = 2(5)+4=14, Bottom=3(5)-1=14 → good.

y + 2 = 2y - 3
Subtract y:
2 = y - 3
Add 3:
y = 5

Left = 5+2=7, Right=2(5)-3=7 → good.

✔ Problem 8:
x = 5, y = 5
Side lengths: Top/Bottom = 14, Left/Right = 7

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Problem 9:
Sides:
Top: 5x - 3
Bottom: 6x - 7
Left: y + 4
Right: 2y - 2

Parallelogram → opposites equal.

5x - 3 = 6x - 7
Subtract 5x:
-3 = x - 7
Add 7:
x = 4

Top = 5(4)-3=17, Bottom=6(4)-7=17 → good.

y + 4 = 2y - 2
Subtract y:
4 = y - 2
Add 2:
y = 6

Left = 6+4=10, Right=2(6)-2=10 → good.

✔ Problem 9:
x = 4, y = 6
Side lengths: Top/Bottom = 17, Left/Right = 10

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All done! Let’s compile final answers clearly.

Final Answer:
Problem 1: x = 7, y = 4; Sides: 26, 7
Problem 2: x = 5, y = 5; Sides: 11, 7
Problem 3: x = 5, y = 4; Sides: 13, 5
Problem 4: x = 4, y = 6; Sides: 13, 10
Problem 5: x = 6, y = 7; Sides: 17, 10
Problem 6: x = 4, y = 4; Sides: 14, 5
Problem 7: x = 5, y = 6; Sides: 17, 11
Problem 8: x = 5, y = 5; Sides: 14, 7
Problem 9: x = 4, y = 6; Sides: 17, 10