Math worksheet for calculating the perimeter and area of trapezoids with given dimensions.

Let’s solve each trapezoid problem one by one. We’ll calculate perimeter (P) and area (A) for each.

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Formulas to remember:

- Perimeter = sum of all side lengths
- Area of a trapezoid = ½ × (base₁ + base₂) × height
→ The two parallel sides are the “bases”. The height is the perpendicular distance between them.

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## Problem 1

Sides: 4 yd, 1.9 yd, 3.8 yd, 4.5 yd
Height = 2.7 yd (given with right angle marks — so it’s perpendicular to bases)

→ Bases are 1.9 yd and 4.5 yd (the top and bottom)

Perimeter:
4 + 1.9 + 3.8 + 4.5 =
4 + 1.9 = 5.9
5.9 + 3.8 = 9.7
9.7 + 4.5 = 14.2 yd

Area:
½ × (1.9 + 4.5) × 2.7
= ½ × 6.4 × 2.7
= 3.2 × 2.7
Let’s compute:
3 × 2.7 = 8.1
0.2 × 2.7 = 0.54
Total = 8.1 + 0.54 = 8.64 sq yd

✔ P = 14.2 yd, A = 8.64 sq yd

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## Problem 2

Sides: 19 yd, 13.2 yd, 19 yd, 7.8 yd
Height = 15.8 yd (perpendicular between bases)

→ Bases: 13.2 yd and 7.8 yd

Perimeter:
19 + 13.2 + 19 + 7.8
Group: (19 + 19) = 38; (13.2 + 7.8) = 21 → Total = 38 + 21 = 59 yd

Area:
½ × (13.2 + 7.8) × 15.8
= ½ × 21 × 15.8
= 10.5 × 15.8

Compute:
10 × 15.8 = 158
0.5 × 15.8 = 7.9
Total = 158 + 7.9 = 165.9 sq yd

✔ P = 59 yd, A = 165.9 sq yd

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## Problem 3

Sides: 9.6 mi, 12.5 mi, 6.3 mi, 11 mi
Height = 10.5 mi (between the two vertical-looking sides? Wait — look at diagram: the height is drawn between the two *parallel* sides — which are the left and right sides? Actually, in this diagram, the height is shown as horizontal dashed line connecting the two non-vertical sides — meaning the *bases* are the left and right sides: 9.6 mi and 6.3 mi? But wait — that doesn’t make sense because they’re not parallel unless it’s rotated.

Actually, looking carefully: the height is labeled 10.5 mi and has right angles on both ends — so it’s perpendicular to the two sides it connects. Those must be the two parallel sides (bases). So the bases are the top and bottom? No — in this diagram, the shape is tilted.

Wait — actually, in trapezoid #3, the two parallel sides are the ones connected by the height — which are the left side (9.6 mi) and right side (6.3 mi)? That can’t be — those aren’t parallel if the height is horizontal.

Actually, let me reinterpret: In standard diagrams, when height is drawn with right-angle markers to two sides, those two sides are the bases (parallel sides). Here, the height is 10.5 mi, and it connects the side labeled 9.6 mi and the side labeled 6.3 mi — but those are not opposite each other.

Wait — no! Looking again: the height is drawn horizontally across the middle, connecting the left slanted side and the right slanted side? That doesn't make sense.

Actually, re-examining: In problem 3, the figure shows a trapezoid where the two parallel sides are the top and bottom? But top is 12.5 mi, bottom is 11 mi? And the height is 10.5 mi — drawn vertically? But the label says "10.5 mi" with a horizontal dashed line — that suggests the height is measured horizontally, meaning the bases are the left and right sides.

This is confusing. Let me think differently.

In any trapezoid, the area formula uses the two parallel sides as bases, and the perpendicular distance between them as height.

In diagram #3, the height is marked as 10.5 mi with right-angle symbols touching the left side (9.6 mi) and the right side (6.3 mi). That implies that the left and right sides are the bases — even though they’re drawn vertically? Or perhaps the figure is rotated.

But geometrically, if the height is perpendicular to two sides, then those two sides are parallel — so yes, the bases are 9.6 mi and 6.3 mi, and height is 10.5 mi.

Then the other two sides (12.5 mi and 11 mi) are the legs.

So:

Perimeter: 9.6 + 12.5 + 6.3 + 11
= (9.6 + 6.3) = 15.9; (12.5 + 11) = 23.5 → total = 15.9 + 23.5 = 39.4 mi

Area: ½ × (9.6 + 6.3) × 10.5
= ½ × 15.9 × 10.5
First, 15.9 × 10.5

Break it down:
15.9 × 10 = 159
15.9 × 0.5 = 7.95
Sum = 159 + 7.95 = 166.95
Then half of that? Wait no — we already have ½ × 15.9 × 10.5 = (15.9 × 10.5)/2

Better:
½ × 15.9 = 7.95
Then 7.95 × 10.5

Compute 7.95 × 10 = 79.5
7.95 × 0.5 = 3.975
Total = 79.5 + 3.975 = 83.475 sq mi

✔ P = 39.4 mi, A = 83.475 sq mi

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## Problem 4

Sides: 14.4 ft, 8.1 ft, 14.8 ft, 7.8 ft
Height = 14 ft (dashed line with right angles — so perpendicular to the two bases)

Which sides are the bases? The height connects the side labeled 7.8 ft and the side labeled 8.1 ft? No — looking at diagram: the height is drawn horizontally between the left and right sides? Actually, the height is labeled 14 ft and has right angles on the top and bottom? Wait — no.

Actually, in diagram #4, the height is drawn as a horizontal dashed line inside the trapezoid, with right-angle marks touching the left side (7.8 ft) and the right side (8.1 ft). So again, the bases are the left and right sides: 7.8 ft and 8.1 ft, and height is 14 ft.

The other two sides are 14.4 ft (top) and 14.8 ft (bottom).

So:

Perimeter: 14.4 + 8.1 + 14.8 + 7.8
Group: (14.4 + 14.8) = 29.2; (8.1 + 7.8) = 15.9 → total = 29.2 + 15.9 = 45.1 ft

Area: ½ × (7.8 + 8.1) × 14
= ½ × 15.9 × 14
= 7.95 × 14

Compute:
7 × 14 = 98
0.95 × 14 = 13.3
Total = 98 + 13.3 = 111.3 sq ft

✔ P = 45.1 ft, A = 111.3 sq ft

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## Problem 5

This one has right angles marked — so it’s a right trapezoid.

Sides: 7.5 mm (left, vertical), 8.6 mm (top), 8.4 mm (right, slanted), 4.3 mm (bottom)

Height = 7.5 mm (since it’s perpendicular to the bases — the top and bottom are horizontal, left side is vertical)

Bases: top = 8.6 mm, bottom = 4.3 mm

Perimeter: 7.5 + 8.6 + 8.4 + 4.3
Add step by step:
7.5 + 8.6 = 16.1
16.1 + 8.4 = 24.5
24.5 + 4.3 = 28.8 mm

Area: ½ × (8.6 + 4.3) × 7.5
= ½ × 12.9 × 7.5
= 6.45 × 7.5

Compute:
6 × 7.5 = 45
0.45 × 7.5 = 3.375
Total = 45 + 3.375 = 48.375 sq mm

✔ P = 28.8 mm, A = 48.375 sq mm

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## Problem 6

Sides: 15.5 mi, 10.1 mi, 15.5 mi, 7.5 mi
Height = 14.5 mi (dashed line with right angles — so perpendicular to the two bases)

Which sides are the bases? The height connects the left side (7.5 mi) and the right side (10.1 mi)? Again, based on right-angle markers, the bases are the two sides that the height is perpendicular to — so 7.5 mi and 10.1 mi.

The other two sides are both 15.5 mi (top and bottom?).

Perimeter: 15.5 + 10.1 + 15.5 + 7.5
Group: (15.5 + 15.5) = 31; (10.1 + 7.5) = 17.6 → total = 31 + 17.6 = 48.6 mi

Area: ½ × (7.5 + 10.1) × 14.5
= ½ × 17.6 × 14.5
= 8.8 × 14.5

Compute:
8 × 14.5 = 116
0.8 × 14.5 = 11.6
Total = 116 + 11.6 = 127.6 sq mi

✔ P = 48.6 mi, A = 127.6 sq mi

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## ✔ Final Answers:

1. P = 14.2 yd, A = 8.64 sq yd
2. P = 59 yd, A = 165.9 sq yd
3. P = 39.4 mi, A = 83.475 sq mi
4. P = 45.1 ft, A = 111.3 sq ft
5. P = 28.8 mm, A = 48.375 sq mm
6. P = 48.6 mi, A = 127.6 sq mi