Area and Perimeter of Various Shapes (up to 1 decimal place; range ... - Free Printable

Let’s solve each shape one by one. We’ll find both the area and the perimeter for each.

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Shape 1: Parallelogram (top left)

- Sides: 2.7 km, 4.4 km, 2.7 km, 4.4 km → opposite sides equal
- Height = 4.2 km (given with dashed line perpendicular to base 2.7 km)

✔ Perimeter = add all sides
= 2.7 + 4.4 + 2.7 + 4.4
= (2.7 + 2.7) + (4.4 + 4.4)
= 5.4 + 8.8 = 14.2 km

✔ Area = base × height
Base = 2.7 km, height = 4.2 km
= 2.7 × 4.2
Let’s calculate:
2.7 × 4 = 10.8
2.7 × 0.2 = 0.54
Total = 10.8 + 0.54 = 11.34 km²

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Shape 2: Trapezoid? Wait — actually it's a parallelogram too! (top right)

Wait — looking again: It has two parallel sides labeled 5.9 mi and 5.6 mi? No — actually, the diagram shows:

It’s a parallelogram with:
- Base = 5.8 mi (dashed line inside, but that’s not a side — wait no!)

Actually, let me re-read the labels:

Top side: 5.9 mi
Right side: 5.6 mi
Inside dashed line: 5.8 mi — this is likely the *height*, since there’s a right angle mark.

But in a parallelogram, area = base × height. Which base? The side perpendicular to the height.

The height is drawn from top to bottom, so it’s perpendicular to the left/right sides? But those are slanted.

Wait — actually, looking at the right-angle symbol: the 5.8 mi is perpendicular to the 5.6 mi side? That doesn’t make sense.

Hold on — perhaps it’s a trapezoid? Let me check the shape again.

Actually, based on standard problems like this, and the fact that it has a right angle marked between the 5.8 mi (dashed) and the 5.6 mi side — that suggests the 5.6 mi is the base, and 5.8 mi is the height.

But then what are the other sides? Top is 5.9 mi, bottom must be same as top if it’s a parallelogram? But 5.9 ≠ 5.6.

Wait — maybe it’s a right trapezoid? With one right angle.

Looking at the diagram description: it has a right angle symbol where the dashed line meets the 5.6 mi side. So probably:

- One vertical side = 5.6 mi (with right angle at bottom)
- Dashed horizontal line = 5.8 mi (this is the height, and also the length of the bottom base?)
- Top side = 5.9 mi

This is confusing without seeing the exact orientation.

Alternative approach: In many such worksheets, when they give you a quadrilateral with a dashed line labeled as “height” and a right angle, and two different top/bottom lengths, it’s a trapezoid.

Assume it’s a trapezoid with:
- Parallel sides: top = 5.9 mi, bottom = ?
Wait — the dashed line is 5.8 mi and is perpendicular to the 5.6 mi side — which might mean the 5.6 mi is the height? No.

I think I made a mistake. Let me reinterpret:

In the top-right shape:
- Left side: not labeled
- Right side: 5.6 mi
- Top: 5.9 mi
- Bottom: not labeled
- Inside: dashed line 5.8 mi with right angle to the right side → so 5.8 mi is perpendicular to 5.6 mi side → meaning 5.6 mi is the base, and 5.8 mi is the height? But then why is top 5.9?

Actually, perhaps it’s a parallelogram after all, and the 5.8 mi is the height corresponding to the base of 5.6 mi.

Yes — that makes sense. Because in a parallelogram, area = base × height, and height must be perpendicular to the base.

So if the 5.6 mi side is the base, and the 5.8 mi is the height (perpendicular to it), then:

✔ Area = 5.6 × 5.8

Calculate:
5.6 × 5 = 28
5.6 × 0.8 = 4.48
Total = 28 + 4.48 = 32.48 mi²

Now perimeter: we need all four sides.

We have top = 5.9 mi, right = 5.6 mi. Since it’s a parallelogram, opposite sides equal:

So bottom = 5.9 mi, left = 5.6 mi

Wait — but then why is the height 5.8? That would only work if the angle is not 90 degrees.

Actually, in a parallelogram, if base is 5.6, and height is 5.8, that’s fine — the side length can be longer than the height.

But then the adjacent side should be calculable via Pythagoras? Not necessary for perimeter.

If it’s a parallelogram, opposite sides are equal.

Given:
- Top = 5.9 mi → so bottom = 5.9 mi
- Right = 5.6 mi → so left = 5.6 mi

Then perimeter = 5.9 + 5.6 + 5.9 + 5.6 = 2×(5.9 + 5.6) = 2×11.5 = 23.0 mi

And area = base × height. Which base? If we take base = 5.6 mi, height = 5.8 mi → area = 5.6 × 5.8 = 32.48 mi²

But is the height corresponding to the 5.6 mi base? The diagram shows the dashed line perpendicular to the 5.6 mi side, so yes.

Okay, proceed.

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Shape 3: Triangle (middle left)

- Base = 4.3 yd
- Height = 4.6 yd (labeled h = 4.6 yd, with right angle to base)
- Other two sides: 4.9 yd and 5.3 yd

✔ Perimeter = sum of all sides = 4.3 + 4.9 + 5.3
= (4.3 + 4.9) = 9.2; 9.2 + 5.3 = 14.5 yd

✔ Area = (base × height) / 2 = (4.3 × 4.6) / 2

First, 4.3 × 4.6:
4 × 4.6 = 18.4
0.3 × 4.6 = 1.38
Total = 18.4 + 1.38 = 19.78
Divide by 2: 19.78 / 2 = 9.89 yd²

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Shape 4: Trapezoid (middle right)

- Parallel sides: top = 7.3 yd, bottom = 7.5 yd
- Height = 7.2 yd (dashed line with right angles to both bases)
- Non-parallel sides: left = 5.1 yd, right = 6.9 yd

✔ Perimeter = 7.3 + 6.9 + 7.5 + 5.1
Add step by step:
7.3 + 6.9 = 14.2
7.5 + 5.1 = 12.6
Total = 14.2 + 12.6 = 26.8 yd

✔ Area of trapezoid = (sum of parallel sides) × height / 2
= (7.3 + 7.5) × 7.2 / 2
= (14.8) × 7.2 / 2

First, 14.8 × 7.2:
14 × 7.2 = 100.8
0.8 × 7.2 = 5.76
Total = 100.8 + 5.76 = 106.56
Divide by 2: 106.56 / 2 = 53.28 yd²

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Shape 5: Trapezoid (bottom left)

- Parallel sides: left = 2.2 mi, right = 2.8 mi? Wait — no.

Looking at labels:
- Left side: 2.2 mi
- Right side: 2.8 mi
- Top: 4.6 mi
- Bottom: 4.5 mi
- Dashed line inside: 4.5 mi — and it’s perpendicular to the left and right sides? There’s a right angle symbol on the left.

Actually, the dashed line is labeled 4.5 mi and has a right angle to the left side (2.2 mi). So likely, the 4.5 mi is the height, and the two parallel sides are the top and bottom? But top is 4.6, bottom is 4.5 — close but not equal.

Wait — perhaps the parallel sides are the left and right? 2.2 and 2.8 — but they are not horizontal.

Standard interpretation: in a trapezoid, the two parallel sides are usually the top and bottom. Here, top = 4.6 mi, bottom = 4.5 mi, and height = 4.5 mi? But the dashed line is 4.5 mi and is perpendicular to the left side.

There’s a right angle between the dashed line and the left side (2.2 mi), so the dashed line is perpendicular to the left side — meaning the left side is vertical? Then the dashed line is horizontal — so it’s the distance between the two non-vertical sides? This is messy.

Alternative: perhaps it’s a trapezoid with parallel sides being the left and right? But 2.2 and 2.8 are different lengths.

Wait — look at the labels again:

- Left side: 2.2 mi (vertical?)
- Right side: 2.8 mi (vertical?)
- Top: 4.6 mi (slanted?)
- Bottom: 4.5 mi (slanted?)
- Dashed line: 4.5 mi — horizontal, connecting left and right, with right angle to left side → so if left side is vertical, dashed line is horizontal → so height is 4.5 mi, and the two parallel sides are the left and right? But they are not parallel if one is 2.2 and other 2.8 unless it's not a rectangle.

I think I got it: this is a trapezoid where the two parallel sides are the top and bottom, but they are not horizontal. However, the height is given as the perpendicular distance between them.

The dashed line is 4.5 mi and is perpendicular to the left side — but if the left side is not perpendicular to the bases, this is confusing.

Perhaps the 4.5 mi dashed line is the height, and it's perpendicular to the two parallel sides. But which are the parallel sides?

Another way: in many diagrams, when they draw a dashed line with a right angle to one side and label it as height, and give two other sides, it's often that the two sides perpendicular to the height are the parallel sides.

Here, the dashed line is 4.5 mi, and it's perpendicular to the left side (2.2 mi) — so if the left side is one base, then the height is 4.5 mi, but then what is the other base?

I recall that in some trapezoids, the height is between the two parallel sides. Let's assume that the top and bottom are the parallel sides: 4.6 mi and 4.5 mi, and the height is the perpendicular distance between them. But the dashed line is labeled 4.5 mi and is shown going from left to right, perpendicular to the left side.

Perhaps the left side is vertical, so the dashed line is horizontal, and thus the height is 4.5 mi, and the two parallel sides are the top and bottom, which are slanted, but their lengths are 4.6 and 4.5, and the distance between them is 4.5 mi? That doesn't make sense because if they are parallel and the distance is 4.5, but their lengths are almost the same, it could be.

For area of trapezoid, we need the lengths of the two parallel sides and the height between them.

Assume that the two parallel sides are the left and right: 2.2 mi and 2.8 mi, and the height is the horizontal distance between them, which is given as 4.5 mi (the dashed line).

That makes sense! Because the dashed line is perpendicular to the left side, and if the left and right are both vertical (parallel), then the horizontal distance between them is the height.

Yes! So:

- Parallel sides: left = 2.2 mi, right = 2.8 mi (both vertical, so parallel)
- Height = horizontal distance between them = 4.5 mi (dashed line)

Then area = (sum of parallel sides) × height / 2 = (2.2 + 2.8) × 4.5 / 2 = (5.0) × 4.5 / 2 = 22.5 / 2 = 11.25 mi²

Perimeter = sum of all sides = left + right + top + bottom = 2.2 + 2.8 + 4.6 + 4.5

Calculate: 2.2 + 2.8 = 5.0; 4.6 + 4.5 = 9.1; total = 5.0 + 9.1 = 14.1 mi

Note: the bottom is labeled 4.5 mi, and the dashed line is also 4.5 mi — but they are different segments. The bottom side is 4.5 mi, and the dashed line (height) is also 4.5 mi — possible.

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Shape 6: Rectangle (bottom right)

- Width = 2 ft
- Height = 3.2 ft

✔ Perimeter = 2 × (width + height) = 2 × (2 + 3.2) = 2 × 5.2 = 10.4 ft

✔ Area = width × height = 2 × 3.2 = 6.4 ft²

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Now, let's compile all answers clearly.

Final Answer:

Shape 1 (Parallelogram):
Area = 11.34 km², Perimeter = 14.2 km

Shape 2 (Parallelogram):
Area = 32.48 mi², Perimeter = 23.0 mi

Shape 3 (Triangle):
Area = 9.89 yd², Perimeter = 14.5 yd

Shape 4 (Trapezoid):
Area = 53.28 yd², Perimeter = 26.8 yd

Shape 5 (Trapezoid):
Area = 11.25 mi², Perimeter = 14.1 mi

Shape 6 (Rectangle):
Area = 6.4 ft², Perimeter = 10.4 ft