Perimeter of Mixed Shapes worksheet with nine different geometric figures and blank lines for calculating perimeter.

Let’s solve each problem one by one. Remember, perimeter means adding up all the sides of a shape.

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Problem 1: Rectangle (8 ft by 15 ft)
A rectangle has two pairs of equal sides.
So, perimeter = 2 × (length + width)
= 2 × (15 + 8)
= 2 × 23
= 46 ft

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Problem 2: Equilateral Triangle (each side 7 in)
All three sides are equal.
Perimeter = 7 + 7 + 7 = 21 in

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Problem 3: Circle (radius = 11 yd)
Use formula: Perimeter (circumference) = 2 × π × r
π = 3.14 (as told)
So, 2 × 3.14 × 11 = 6.28 × 11
Let’s calculate:
6 × 11 = 66
0.28 × 11 = 3.08
Total = 66 + 3.08 = 69.08 yd

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Problem 4: Parallelogram (sides 16 in and 9 in)
Opposite sides are equal.
Perimeter = 2 × (16 + 9) = 2 × 25 = 50 in

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Problem 5: Square (side = 5 yd)
All four sides equal.
Perimeter = 4 × 5 = 20 yd

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Problem 6: Trapezoid (sides: 13 ft, 7 ft, 19 ft, 10 ft)
Just add all sides:
13 + 7 = 20
19 + 10 = 29
20 + 29 = 49 ft

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Problem 7: Quadrilateral (sides: 3 yd, 11 yd, and two others marked with same tick marks — so they’re equal to the ones shown?)
Wait — looking at the diagram: it shows two sides labeled “3 yd” and “11 yd”, and the other two sides have matching tick marks — meaning opposite sides are equal? Actually, in this case, since it's drawn like a kite or irregular quad, but the ticks show that the two unlabelled sides are equal to the labelled ones? Let me recheck.

Actually, in Problem 7: The figure has:
- One side = 3 yd
- Adjacent side = 11 yd
- Then another side with double tick mark → same as the 3 yd side? No — wait, standard notation: single tick = same length, double tick = same length.

Looking again:
It appears there are two sides with single tick (so both 3 yd), and two sides with double tick (both 11 yd). So it’s a parallelogram-like shape? Or just a quadrilateral with opposite sides equal.

So perimeter = 3 + 11 + 3 + 11 = 28 yd

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Problem 8: Pentagon? Wait — actually, it’s a pentagon? No — count the sides: 5 sides? Let’s see:

Sides given: 9 ft, 10 ft, 16 ft, and then two more with tick marks.

Actually, looking:
Left side: 9 ft
Top-left: 10 ft
Right side: 16 ft
Bottom-right: ? (but has same tick as top-left → so also 10 ft?)
Bottom-left: ? (same tick as left side → so also 9 ft?)

Wait — no, let’s label:

From bottom-left going clockwise:
- Bottom-left vertical: 9 ft (with single tick)
- Top-left slanted: 10 ft (with double tick)
- Right vertical: 16 ft (no tick? But maybe it’s unique)
Wait — actually, in the image, the right side is 16 ft, and the bottom-right side has a double tick — same as top-left → so 10 ft. And the bottom-left has single tick — same as left side → 9 ft.

But we already have left side = 9 ft, top-left = 10 ft, right = 16 ft, bottom-right = 10 ft (double tick), bottom-left = 9 ft (single tick).

Wait — that would be 5 sides? Let me recount the vertices.

Actually, it’s a pentagon? No — looking at the drawing: it’s a 5-sided polygon? Or 4?

Wait — better approach: list all sides with their lengths based on ticks.

In Problem 8:
- Left side: 9 ft (marked with one tick)
- Top side: 10 ft (marked with two ticks)
- Right side: 16 ft (no tick — so unique)
- Bottom-right side: marked with two ticks → so same as top → 10 ft
- Bottom-left side: marked with one tick → same as left → 9 ft

So sides: 9, 10, 16, 10, 9 → that’s five sides? But that doesn’t make sense for a simple shape.

Wait — perhaps I miscounted. Let me think differently.

Actually, looking at typical problems like this, it’s likely a trapezoid or irregular quadrilateral. But the diagram shows 5 segments? No — let me visualize:

The shape in #8 looks like a house without the roof peak — actually, it’s a pentagon? Or maybe it’s a quadrilateral with an extra line? No.

Wait — perhaps it’s a 4-sided figure where two sides are split? No.

Alternative: Maybe the "16 ft" is the entire right side, and the bottom is made of two parts? But the problem says “find perimeter”, so we add all outer edges.

Given the ticks:

Assume:
- Side A: 9 ft (left, single tick)
- Side B: 10 ft (top, double tick)
- Side C: 16 ft (right, no tick — so different)
- Side D: ? (bottom-right, double tick → so 10 ft)
- Side E: ? (bottom-left, single tick → so 9 ft)

That’s 5 sides: 9 + 10 + 16 + 10 + 9 = 54 ft

But that seems odd. Perhaps the 16 ft includes part of the bottom? No — in perimeter, we go around the outside.

I think it’s safe to assume from the tick marks that:

There are two sides of 9 ft (single tick), two sides of 10 ft (double tick), and one side of 16 ft.

So total = 9 + 9 + 10 + 10 + 16 = let’s add: 9+9=18, 10+10=20, 18+20=38, +16=54 ft

Yes.

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Problem 9: Rhombus? All sides equal?

Diagram shows all four sides have the same tick mark → so all sides equal.

One side labeled 19 in → so all sides 19 in.

Perimeter = 4 × 19 = 76 in

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Now, let’s compile all answers:

1) 46 ft
2) 21 in
3) 69.08 yd
4) 50 in
5) 20 yd
6) 49 ft
7) 28 yd
8) 54 ft
9) 76 in

Double-checking calculations:

1) 2*(15+8)=2*23=46 ✔️
2) 7*3=21 ✔️
3) 2*3.14*11=6.28*11: 6*11=66, 0.28*11=3.08, total 69.08 ✔️
4) 2*(16+9)=2*25=50 ✔️
5) 4*5=20 ✔️
6) 13+7+19+10= let's add: 13+7=20, 19+10=29, 20+29=49 ✔️
7) 3+11+3+11=28 ✔️
8) 9+10+16+10+9=54 ✔️ (assuming 5 sides as per ticks)
9) 4*19=76 ✔️

All correct.

Final Answer:
1) 46 ft
2) 21 in
3) 69.08 yd
4) 50 in
5) 20 yd
6) 49 ft
7) 28 yd
8) 54 ft
9) 76 in