Geometry Worksheets | Area Worksheets - Free Printable

Let’s solve each problem one by one. We’ll calculate the Area and Perimeter, and identify the Type of quadrilateral for each.

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Problem 1: Trapezoid (with sides a1, a2, b1, b2, height h)

Given:
- a1 = 8.7 ft
- a2 = 4.1 ft
- b1 = 5.86 ft
- b2 = 4.23 ft
- h = 4.2 ft

This is a trapezoid with two parallel bases (a1 and a2) and non-parallel legs (b1 and b2).

Area of trapezoid = (base1 + base2) × height ÷ 2
= (8.7 + 4.1) × 4.2 ÷ 2
= 12.8 × 4.2 ÷ 2
= 53.76 ÷ 2
= 26.88 ft²

Perimeter = sum of all sides = a1 + a2 + b1 + b2
= 8.7 + 4.1 + 5.86 + 4.23
= 12.8 + 10.09
= 22.89 ft

Type: Trapezoid

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Problem 2: Parallelogram

Given:
- a = 4.38 yds (side)
- c = 9.9 yds (base)
- h = 4.1 yds (height)

In parallelograms, opposite sides are equal. So sides are: a, c, a, c → but wait — in diagram, “a” is slanted side, “c” is base. So perimeter = 2×(a + c)

But note: area uses base × height → here base is c = 9.9 yds, height = 4.1 yds

Area = base × height = 9.9 × 4.1
= let’s compute: 10 × 4.1 = 41, minus 0.1×4.1=0.41 → 41 - 0.41 = 40.59 yd²

Wait — actually: 9.9 × 4.1
Break it down:
9 × 4.1 = 36.9
0.9 × 4.1 = 3.69
Total = 36.9 + 3.69 = 40.59 yd²

Perimeter = 2 × (side a + side c) = 2 × (4.38 + 9.9)
= 2 × 14.28 = 28.56 yds

Type: Parallelogram

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Problem 3: Square

Given: s = 6.8 mm

All sides equal, angles 90°.

Area = s² = 6.8 × 6.8
= (7 - 0.2)² = 49 - 2×7×0.2 + 0.04 = 49 - 2.8 + 0.04 = 46.24? Wait, better to multiply directly:

6.8 × 6.8
= 6 × 6 = 36
6 × 0.8 = 4.8 → twice = 9.6
0.8 × 0.8 = 0.64
Total = 36 + 9.6 + 0.64 = 46.24 mm²

Or: 68 × 68 = 4624 → so 6.8 × 6.8 = 46.24 ✔️

Perimeter = 4 × s = 4 × 6.8 = 27.2 mm

Type: Square

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Problem 4: Rhombus (all sides equal, labeled ‘a’, height ‘h’)

Given:
- a = 5.5 inches (all sides same)
- h = 5.02 inches

Since all sides are equal, this is a rhombus.

Area = base × height = a × h = 5.5 × 5.02
Compute:
5 × 5.02 = 25.1
0.5 × 5.02 = 2.51
Total = 25.1 + 2.51 = 27.61 in²

Perimeter = 4 × a = 4 × 5.5 = 22 inches

Type: Rhombus

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Problem 5: Rectangle

Given:
- a = 7.9 inches (length)
- b = 4.8 inches (width)

Opposite sides equal, right angles.

Area = length × width = 7.9 × 4.8
Compute:
8 × 4.8 = 38.4
Minus 0.1 × 4.8 = 0.48 → 38.4 - 0.48 = 37.92 in²

Or: 7.9 × 4.8
= (8 - 0.1)(5 - 0.2) = too messy — just do:

7.9 × 4 = 31.6
7.9 × 0.8 = 6.32
Total = 31.6 + 6.32 = 37.92 in²

Perimeter = 2 × (length + width) = 2 × (7.9 + 4.8) = 2 × 12.7 = 25.4 inches

Type: Rectangle

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Problem 6: Parallelogram

Given:
- a = 4.42 ft (slant side)
- c = 10 ft (base)
- h = 4.2 ft (height)

Same as problem 2.

Area = base × height = 10 × 4.2 = 42 ft²

Perimeter = 2 × (a + c) = 2 × (4.42 + 10) = 2 × 14.42 = 28.84 ft

Type: Parallelogram

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Problem 7: Square

Given: s = 5.1 yds

Area = s² = 5.1 × 5.1
= (5 + 0.1)² = 25 + 2×5×0.1 + 0.01 = 25 + 1 + 0.01 = 26.01 yd²

Perimeter = 4 × s = 4 × 5.1 = 20.4 yds

Type: Square

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Problem 8: Rectangle

Given:
- a = 8.7 cm (length)
- b = 4.6 cm (width)

Area = 8.7 × 4.6
Compute:
8 × 4.6 = 36.8
0.7 × 4.6 = 3.22
Total = 36.8 + 3.22 = 40.02 cm²

Perimeter = 2 × (8.7 + 4.6) = 2 × 13.3 = 26.6 cm

Type: Rectangle

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Problem 9: Parallelogram

Given:
- a = 5 mm (side)
- h = 4.6 mm (height)

Note: In diagram, base is also labeled ‘a’? Wait — looking at diagram: it shows side ‘a’ and height ‘h’, and base is also ‘a’? That would mean it's a rhombus? But only one side given.

Actually, in problem 9, it says:
“a = 5 mm” and “h = 4.6 mm”

And diagram shows a parallelogram with side labeled ‘a’, and height ‘h’. But for area, we need base × height. If the base is also ‘a’, then yes.

Assuming base = a = 5 mm (since no other base given), then:

Area = base × height = 5 × 4.6 = 23 mm²

Perimeter: Since it’s a parallelogram, we need both adjacent sides. But only one side ‘a’ is given. However, in the diagram, it looks like both pairs of sides are labeled ‘a’? Wait — no, in problem 9, only ‘a’ is given, and it’s used for side and possibly base.

Looking back at original image description: for problem 9, it says “a = 5 mm”, and diagram has side labeled ‘a’, and base also seems to be ‘a’? Actually, in many such diagrams, if only one side is given and it’s a parallelogram, sometimes they imply it’s a rhombus? But not necessarily.

Wait — re-examining: in problem 9, the label under the figure says “a = 5 mm”, and the figure has two sides labeled ‘a’? Actually, in the user’s text: “9) ... a = 5 mm h = 4.6 mm”

And in the diagram description earlier, for similar problems, when it’s a parallelogram with only one side given, but height, we assume the base is that side? Or perhaps it’s a rhombus?

But in problem 4, it was clearly a rhombus because all sides were labeled ‘a’. Here, only one ‘a’ is mentioned, but in the diagram, likely both adjacent sides are ‘a’? No — let me think differently.

Actually, in standard notation for such worksheets, if a parallelogram has side ‘a’ and base ‘c’, but here only ‘a’ is given. Perhaps it’s a typo or assumption.

Wait — look at problem 2 and 6: they gave both ‘a’ and ‘c’. Here only ‘a’ is given. But in the diagram for problem 9, it might be that the base is also ‘a’? Or perhaps it’s a rhombus.

To resolve: since only one side length is provided, and it’s called ‘a’, and in the context, likely it’s intended that both pairs of sides are equal? But that would make it a rhombus.

Alternatively, maybe the base is ‘a’ and the slant side is different — but not given. That can’t be.

Another possibility: in some diagrams, ‘a’ is used for the base, and the side is not needed for area, but for perimeter we need both.

I think there’s an issue. Let me check the original problem statement again.

User wrote for problem 9: “a = 5 mm h = 4.6 mm”

And in the diagram description, it’s similar to problem 2 and 6, which had ‘a’ and ‘c’. But here only ‘a’ is given.

Perhaps it’s a mistake, or perhaps in this case, the parallelogram has sides ‘a’ and another side not given? That doesn’t work.

Wait — looking at the pattern: in problem 4, it was a rhombus with all sides ‘a’. In problem 9, the diagram might show a parallelogram where the base is ‘a’ and the side is also ‘a’? Unlikely.

Perhaps ‘a’ is the base, and the side is not specified, but for perimeter, we can’t calculate without both.

This is ambiguous. But let’s look at the diagram description from the user: for problem 9, it says “a = 5 mm”, and in the figure, it’s drawn with side labeled ‘a’, and height ‘h’, and base also seems to be labeled ‘a’? In many such worksheets, if only one dimension is given for a parallelogram besides height, and it’s called ‘a’, it might be assumed that the base is ‘a’, and the side is different — but not given.

That can’t be. Perhaps it’s a rhombus? But then why not say so.

Another idea: in problem 9, the label “a” might refer to the base, and the side is not needed for area, but for perimeter, we need the side length. Since it’s not given, perhaps we assume it’s the same as problem 4? But that’s not fair.

Let me double-check the user input: "9) ... a = 5 mm h = 4.6 mm"

And in the initial list, for problem 2: "a = 4.38 yds c = 9.9 yds h = 4.1 yds" — so two sides given.

For problem 6: "a = 4.42 ft c = 10 ft h = 4.2 ft"

For problem 9, only 'a' is given. This suggests that perhaps in problem 9, the parallelogram has both pairs of sides equal to 'a', i.e., it's a rhombus. That makes sense because otherwise perimeter can't be calculated.

In problem 4, it was explicitly a rhombus with all sides 'a'. Here, similarly, likely it's intended to be a rhombus.

Moreover, in the diagram, if it's drawn with all sides equal, then yes.

So I'll assume it's a rhombus with side a = 5 mm.

Then:

Area = base × height = 5 × 4.6 = 23 mm²

Perimeter = 4 × a = 4 × 5 = 20 mm

Type: Rhombus

If it were not a rhombus, we couldn't find perimeter, so this must be it.

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Now, compiling all answers:

1) Area: 26.88 ft², Perimeter: 22.89 ft, Type: Trapezoid
2) Area: 40.59 yd², Perimeter: 28.56 yds, Type: Parallelogram
3) Area: 46.24 mm², Perimeter: 27.2 mm, Type: Square
4) Area: 27.61 in², Perimeter: 22 in, Type: Rhombus
5) Area: 37.92 in², Perimeter: 25.4 in, Type: Rectangle
6) Area: 42 ft², Perimeter: 28.84 ft, Type: Parallelogram
7) Area: 26.01 yd², Perimeter: 20.4 yds, Type: Square
8) Area: 40.02 cm², Perimeter: 26.6 cm, Type: Rectangle
9) Area: 23 mm², Perimeter: 20 mm, Type: Rhombus

Final Answer:
1) Area: 26.88 ft², Perimeter: 22.89 ft, Type: Trapezoid
2) Area: 40.59 yd², Perimeter: 28.56 yds, Type: Parallelogram
3) Area: 46.24 mm², Perimeter: 27.2 mm, Type: Square
4) Area: 27.61 in², Perimeter: 22 in, Type: Rhombus
5) Area: 37.92 in², Perimeter: 25.4 in, Type: Rectangle
6) Area: 42 ft², Perimeter: 28.84 ft, Type: Parallelogram
7) Area: 26.01 yd², Perimeter: 20.4 yds, Type: Square
8) Area: 40.02 cm², Perimeter: 26.6 cm, Type: Rectangle
9) Area: 23 mm², Perimeter: 20 mm, Type: Rhombus