Area of Quadrilateral Worksheets - Free Printable

Let’s solve each problem one by one.

---

Problem 1:

Shape: A trapezium (trapezoid)
Top = 12 cm, Bottom = 10 cm, Height = 4 cm
Use formula: Area = ½ × (top + bottom) × height
→ Area = ½ × (12 + 10) × 4
→ Area = ½ × 22 × 4
→ Area = 11 × 4 = 44 cm²

---

Problem 2:

Shape: Trapezium
Top = 10 m, Bottom = 6 m, Height = 5 m
Area = ½ × (10 + 6) × 5
→ Area = ½ × 16 × 5
→ Area = 8 × 5 = 40 m²

---

Problem 3:

Shape: Parallelogram
Base = 11 mm, Height = 7 mm
Area = base × height
→ Area = 11 × 7 = 77 mm²

---

Problem 4:

Shape: Kite or rhombus split into two triangles by diagonal
Diagonals: 9 m and 3 m
Area of kite = ½ × d1 × d2
→ Area = ½ × 9 × 3 = ½ × 27 = 13.5 m²

*(Note: The hint doesn’t give this formula, but since it’s made of two triangles sharing the 9m base, each with height 3m total? Wait — actually, looking at the diagram: the 3m is the perpendicular height from top to the 9m line. So it’s two triangles on the same base 9m, each with height 3m? No — the 3m is the full height from top to bottom across the shape. Actually, if you split along the 9m line, you get two triangles, each with base 9m and height 3m? That would be wrong because then total area = 2 × (½ × 9 × 3) = 27 — too big.

Wait — re-read: the 3m is labeled as the vertical distance from the top vertex to the horizontal diagonal (9m). So the shape is symmetric? Then it’s two triangles, each with base 9m and height 3m? But that would mean the total height is 3m, so each triangle has height 1.5m? No — the label says “3m” with an arrow pointing from top to the 9m line — meaning the perpendicular height for the top triangle is 3m? But then what about the bottom?

Actually, looking again: the 3m is likely the height of the entire shape relative to the 9m base? Or perhaps it’s a kite where the 9m is one diagonal and 3m is half the other? Hmm.

Wait — standard formula for kite: Area = ½ × d1 × d2. If 9m and 3m are the two diagonals, then area = ½ × 9 × 3 = 13.5 m². And since the diagram shows 3m as the perpendicular from top to the 9m line, and assuming symmetry, the full other diagonal is 6m? But it’s labeled 3m — probably meaning the full height is 3m? Let me think differently.

Alternative approach: Split the shape into two triangles along the 9m line. Each triangle has base 9m and height 3m? But that would make area = 2 × (½ × 9 × 3) = 27 — which seems too large.

Wait — no: if the 3m is the perpendicular distance from the top vertex to the 9m line, and similarly there’s a bottom vertex, but the diagram only labels 3m — perhaps it’s implying that the total height is 3m? Actually, in many such diagrams, when they show a diamond shape with a horizontal diagonal and a vertical arrow labeled 3m, it means the perpendicular height from top to bottom is 3m, and the base is 9m — but that would be for a parallelogram.

I think I made a mistake. Looking at problem 4: it’s a kite shape, with a horizontal line labeled 9m (probably the longer diagonal), and a vertical arrow labeled 3m from the top vertex down to that line — meaning the height of the top triangle is 3m. But since it’s symmetric, the bottom triangle also has height 3m? Then total height is 6m? But that contradicts the label.

Actually, in standard notation, if they draw a vertical arrow from top to the horizontal diagonal and label it 3m, it usually means the perpendicular height for that triangle is 3m. Since the shape is symmetric, the bottom triangle also has height 3m. So total area = area of top triangle + area of bottom triangle = 2 × (½ × 9 × 3) = 27 m².

But wait — that can’t be right because then the height of the whole shape is 6m, but they only labeled 3m. Perhaps the 3m is the full height? Let me check online or recall: in some diagrams, they label the height from top to bottom as 3m, and the base as 9m — but that would be for a parallelogram.

Another way: perhaps the 9m is the base, and 3m is the height — so area = base × height = 9 × 3 = 27 m². But that’s for a parallelogram, not a kite.

I think I need to go with the most logical interpretation. In problem 4, the shape is a kite, and the 9m is one diagonal, and the 3m is half the other diagonal? No, the arrow goes from top to the 9m line, suggesting it's the height.

Let me look at problem 5 for comparison: it has a similar shape, with 11cm horizontal and 5cm vertical from top to the line. In problem 5, if we use the kite formula, area = ½ × 11 × 5 = 27.5 cm², which makes sense.

Similarly, for problem 4, if 9m and 3m are the two diagonals, area = ½ × 9 × 3 = 13.5 m².

And in the diagram, the 3m is likely the full length of the other diagonal, not the height. Because if it were the height, they would have specified "height", but here it's just a dimension.

In many textbooks, for a kite, they show the two diagonals. So I'll assume 9m and 3m are the diagonals.

So area = ½ × 9 × 3 = 13.5 m².

But let's confirm with the hint: the hint gives formulas for parallelogram and trapezium, but not for kite. However, the instruction says "split them up into rectangles and triangles". For problem 4, if we split along the 9m line, we get two triangles, each with base 9m and height... if the 3m is the perpendicular from top to the 9m line, then for the top triangle, height is 3m, but for the bottom triangle, if it's symmetric, height is also 3m, so total area = 2 × (½ × 9 × 3) = 27 m².

This is confusing. Let me think of the shape: it's a diamond, with a horizontal line of 9m, and a vertical arrow from the top vertex to that line labeled 3m. This suggests that the perpendicular distance from the top vertex to the 9m line is 3m. Since the shape is symmetric, the bottom vertex is also 3m below the 9m line, so the total height is 6m. But that doesn't make sense because then the area would be large.

Perhaps the 3m is the height of the entire shape, and the 9m is the base. But for a kite, it's not a parallelogram.

I recall that for any quadrilateral with perpendicular diagonals, area = ½ × d1 × d2. In this case, if the diagonals are 9m and 3m, and they are perpendicular, then area = ½ × 9 × 3 = 13.5 m².

And in the diagram, the 3m is likely the length of the vertical diagonal, not the height. Because if it were the height, they would have drawn it differently.

In problem 5, it's the same: 11cm horizontal, 5cm vertical from top to the line — and if we assume the vertical is the other diagonal, then area = ½ × 11 × 5 = 27.5 cm².

So for consistency, in problem 4, area = ½ × 9 × 3 = 13.5 m².

I'll go with that.

---

Problem 5:

Shape: Kite
Diagonals: 11 cm and 5 cm
Area = ½ × 11 × 5 = 55/2 = 27.5 cm²

---

Problem 6:

Shape: Parallelogram
Base = 30 mm, Height = 9 mm
Area = base × height = 30 × 9 = 270 mm²

---

Now, let's list all answers:

1) 44 cm²
2) 40 m²
3) 77 mm²
4) 13.5 m²
5) 27.5 cm²
6) 270 mm²

Double-checking problem 4: if the shape is split into two triangles by the 9m line, and each triangle has height 3m (since the vertical arrow is from top to the line, and assuming symmetry, the bottom is also 3m), then area = 2 * (0.5 * 9 * 3) = 27 m². But that would mean the total height is 6m, which is not indicated.

Perhaps the 3m is the height of the whole shape, and the 9m is the base, but for a kite, it's not straightforward.

Another thought: in some diagrams, the vertical arrow labeled 3m might mean the distance from the top to the bottom is 3m, and the 9m is the width at the middle. But for a kite, the area is still ½ * d1 * d2.

I think the intended interpretation is that 9m and 3m are the two diagonals. Because in problem 5, it's clearly diagonals: 11cm and 5cm, and area is ½*11*5=27.5.

Similarly, for problem 4, 9m and 3m are diagonals, so area = ½*9*3=13.5 m².

I'll stick with that.

Final answers:

1) 44 cm²
2) 40 m²
3) 77 mm²
4) 13.5 m²
5) 27.5 cm²
6) 270 mm²

All units are correct as per the problems.

Final Answer:
1) 44 cm²
2) 40 m²
3) 77 mm²
4) 13.5 m²
5) 27.5 cm²
6) 270 mm²