Drawing Shapes on a Grid - Worksheet | Maths Year 4 - Free Printable

Let’s solve each shape one by one. We’ll plot the points on the grid (mentally or on paper), connect them in order, and see what shape we get.

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Shape 1: Points are (1,5), (1,1), (4,1)

- Plot (1,5): go right 1, up 5 → top left area
- Plot (1,1): go right 1, up 1 → same x as above, but lower
- Plot (4,1): go right 4, up 1 → same y as previous, further right

Now connect them:
- From (1,5) to (1,1): vertical line down
- From (1,1) to (4,1): horizontal line right
- To close the shape, we need to go from (4,1) back to (1,5). That’s a diagonal.

Wait — that’s only 3 points. So it’s a triangle? But let’s check if it’s closed properly.

Actually, when you connect these three points, you get a right-angled triangle:
- Right angle at (1,1) because one side is vertical, one is horizontal.
- The third side is the hypotenuse from (4,1) to (1,5).

✔ Shape 1: Triangle

But wait — maybe they expect us to assume we connect back to start? Yes, always close the shape.

So yes — 3 points = triangle.

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Shape 2: Points are (1,3), (2,5), (4,5), (6,3)

Plot them:

- (1,3)
- (2,5)
- (4,5)
- (6,3)

Connect in order:

From (1,3) → (2,5): up and right
(2,5) → (4,5): horizontal right
(4,5) → (6,3): down and right
Then back to (1,3)? Wait — that would be a long diagonal.

Actually, let’s think about symmetry.

Notice:
- (2,5) and (4,5) are at same height → top edge
- (1,3) and (6,3) are at same height → bottom edge? Not exactly — (1,3) and (6,3) are both y=3, so yes!

Wait — actually, connecting:

(1,3) → (2,5) → (4,5) → (6,3) → back to (1,3)

This makes a quadrilateral with two parallel sides? Let’s check slopes.

Top: from (2,5) to (4,5) → slope 0 (horizontal)

Bottom: from (1,3) to (6,3) → also slope 0 → so top and bottom are parallel.

Left side: (1,3) to (2,5): rise 2, run 1 → slope 2

Right side: (4,5) to (6,3): rise -2, run 2 → slope -1 → not same as left.

Wait — that means it’s a trapezoid? Because only one pair of sides is parallel? Actually, top and bottom are both horizontal → so yes, parallel.

But let me double-check the connections. Maybe I should draw it mentally.

Points:

A(1,3), B(2,5), C(4,5), D(6,3)

Connect A-B-C-D-A

AB: from (1,3) to (2,5) — steep up
BC: (2,5) to (4,5) — flat right
CD: (4,5) to (6,3) — down-right
DA: (6,3) to (1,3) — flat left? Wait no — (6,3) to (1,3) is horizontal left, but that skips the connection.

Actually, in polygon drawing, we connect consecutive points and then last to first.

So sides are AB, BC, CD, DA.

DA is from (6,3) to (1,3) — which is horizontal left.

But then we have two horizontal sides: BC (top) and DA (bottom). Both horizontal → parallel.

And the other two sides: AB and CD — not parallel.

So this is a trapezoid.

But wait — is it symmetric? Let’s see midpoints.

Alternatively, maybe it’s a kite? No.

Another way: count the sides — 4 sides → quadrilateral. With one pair of parallel sides → trapezoid.

Yes.

✔ Shape 2: Trapezoid

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Shape 3: Points are (1,4), (2,2), (3,5), (4,2), (5,4)

That’s 5 points → pentagon?

Plot them:

- (1,4)
- (2,2)
- (3,5) ← highest point
- (4,2)
- (5,4)

Connect in order:

(1,4) → (2,2): down-right
(2,2) → (3,5): up-right
(3,5) → (4,2): down-right
(4,2) → (5,4): up-right
(5,4) → back to (1,4): left horizontal? From (5,4) to (1,4) is horizontal left.

Wait — but (5,4) to (1,4) is a straight line across the top? But we already have (1,4) and (5,4) at same height.

Actually, looking at the points:

It looks like a star? Or a house with a roof?

Wait — let’s list them again:

Start at (1,4)
Down to (2,2)
Up to (3,5) — peak
Down to (4,2)
Up to (5,4)
Back to (1,4)

If you connect these, it forms a symmetrical shape with a point at the top (3,5), and base from (1,4) to (5,4), but dipping down at (2,2) and (4,2).

Actually, this looks like a pentagon, but more specifically, it might be a house-shaped pentagon or just a regular pentagon? No, not regular.

But since it has 5 vertices, it’s a pentagon.

Is there a better name? Sometimes called an "arrowhead" or "chevron", but for school level, probably just pentagon.

Wait — let me visualize:

Imagine plotting:

At x=1,y=4; x=2,y=2; x=3,y=5; x=4,y=2; x=5,y=4

Connecting them in order gives a shape that goes down, up to peak, down, up, then back left.

Actually, this is a symmetrical pentagon that looks like a crown or a mountain range.

But for elementary math, they likely just want the number of sides.

5 sides → pentagon.

✔ Shape 3: Pentagon

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Shape 4: Points are (1,1), (2,3), (5,1), (6,3)

Plot:

- (1,1)
- (2,3)
- (5,1)
- (6,3)

Connect in order:

(1,1) → (2,3): up-right
(2,3) → (5,1): down-right
(5,1) → (6,3): up-right
(6,3) → back to (1,1): down-left diagonal

Check for parallel sides.

Side 1: (1,1) to (2,3): rise 2, run 1 → slope 2
Side 2: (2,3) to (5,1): rise -2, run 3 → slope -2/3
Side 3: (5,1) to (6,3): rise 2, run 1 → slope 2 → same as side 1!
Side 4: (6,3) to (1,1): rise -2, run -5 → slope (-2)/(-5) = 2/5

So sides 1 and 3 both have slope 2 → they are parallel.

Sides 2 and 4 have different slopes → not parallel.

So we have one pair of parallel sides → trapezoid.

Also, notice: (1,1) and (5,1) are at same y-level? No, (1,1) and (5,1) are both y=1, but they are not directly connected.

Actually, the two parallel sides are the “slanted” ones: from (1,1)-(2,3) and (5,1)-(6,3). Both go up 2, right 1.

The other two sides cross between them.

So yes — trapezoid.

But wait — is it a parallelogram? For that, both pairs of opposite sides must be parallel. Here, only one pair is parallel → so trapezoid.

✔ Shape 4: Trapezoid

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Final check:

Shape 1: 3 points → triangle
Shape 2: 4 points, one pair parallel sides → trapezoid
Shape 3: 5 points → pentagon
Shape 4: 4 points, one pair parallel sides → trapezoid

All make sense.

Final Answer:
1. Triangle
2. Trapezoid
3. Pentagon
4. Trapezoid