Shapes Worksheet (with answers)

Shapes

discia.org 10 questions · 20 marks

Name Date

Either paper 2 marks

A polygon is named after the number of sides it has.

(a)
A polygon has \(8\) sides.

Write down the mathematical name of the polygon.

(b)
How many sides does a quadrilateral have?

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(a) octagon
(b) \(4\ \text{sides}\)

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Either paper 1 mark

Here is a quadrilateral. It is drawn accurately.

State the mathematical name of the quadrilateral.

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rhombus

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Either paper 1 mark

Hafsa is thinking of a quadrilateral. She says:

"My shape has opposite sides that are equal and parallel, no right angles, and no lines of symmetry."

State the mathematical name of Hafsa's quadrilateral.

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parallelogram

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Either paper 2 marks

Here is a regular decagon.

(a)
State the number of lines of symmetry of the shape.

(b)
State the order of rotational symmetry of the shape.

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(a) \(10\ \text{lines}\)
(b) \(10\)

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Either paper 2 marks

The diagram shows an isosceles trapezium.

(a)
Write down the number of lines of symmetry of the isosceles trapezium.

(b)
Write down the order of rotational symmetry of the isosceles trapezium.

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(a) \(1\)
(b) \(1\)

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Either paper 3 marks

The diagram shows the quadrilateral \(DEFG\).

(a)
Write down the side that is parallel to \(DE\).

(b)
Write down the side that is perpendicular to \(DE\).

(c)
Write down the mathematical name of the quadrilateral \(DEFG\).

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(a) \(GF\)
(b) \(DG\)
(c) trapezium

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Either paper 3 marks

Here is a right-angled triangle on a numbered square grid. Its right angle is at the origin.

You may turn the triangle over, rotate it, or do both. Copies of the triangle must fit edge to edge with no gaps and no overlaps.

(a)
On a square grid, show how you can make a parallelogram with two of these triangles.

A rectangle counts as a parallelogram.

(b)
On a square grid, show how you can make a trapezium with three of these triangles.

(c)
On a square grid, show how you can make a rhombus with four of these triangles.

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(a) Any arrangement of two copies whose outline is a parallelogram is correct. For example, two triangles sharing the vertical side, the second rotated half a turn about the middle of that side, with outline \((0, 0)\), \((4, 0)\), \((0, 7)\), \((-4, 7)\). Others: a half turn about the middle of the horizontal side, with outline \((0, 7)\), \((0, 0)\), \((4, -7)\), \((4, 0)\); or two copies joined along their hypotenuse to make the \(4\) by \(7\) rectangle \((0, 0)\), \((4, 0)\), \((4, 7)\), \((0, 7)\).
(b) Any arrangement of three copies whose outline is a trapezium is correct. For example, take the parallelogram from part (a) and add a third triangle with corners \((-4, 0)\), \((0, 0)\), \((-4, 7)\), giving the outline \((-4, 0)\), \((4, 0)\), \((0, 7)\), \((-4, 7)\). Another: add a third triangle with corners \((0, 0)\), \((0, -7)\), \((4, -7)\) to the half-turn parallelogram \((0, 7)\), \((0, 0)\), \((4, -7)\), \((4, 0)\), giving the outline \((0, 7)\), \((0, -7)\), \((4, -7)\), \((4, 0)\), whose vertical parallel sides are \(14\) and \(7\) squares long.
(c) Four triangles with their right angles meeting at one point, each a reflection of the next. Taking that point as the origin, the outline has vertices \((4, 0)\), \((0, 7)\), \((-4, 0)\) and \((0, -7)\).

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Either paper 1 mark

Rosa draws a quadrilateral. Its two diagonals cut each other exactly in half and cross at right angles, but are not equal in length.

State the mathematical name of Rosa's quadrilateral.

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rhombus

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Either paper 2 marks

In the grid below, shade one quarter of the squares so that the grid has exactly two lines of symmetry. Shade complete squares only.

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Any shading of 10 squares that leaves the grid with exactly two lines of symmetry

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Either paper 3 marks

Quadrilateral \(ABCD\) has

- angle \(ABC = 90^\circ\) - \(BC = 2\) cm - \(CD\) is parallel to \(BA\) - \(CD = 3\) cm

\(AB\) has been drawn for you on the centimetre grid.

Plot the points \(C\) and \(D\) on the grid to complete \(ABCD\).

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C(4, 5) and D(7, 5), with A, B, C, D joined in order (or, on the other side of AB, C(4, 1) and D(7, 1))
Also right:

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discia.org Shapes · sheet 1

Answers Shapes · sheet 1

(a) octagon
(b) \(4\ \text{sides}\)
rhombus
parallelogram
(a) \(10\ \text{lines}\)
(b) \(10\)
(a) \(1\)
(b) \(1\)
(a) \(GF\)
(b) \(DG\)
(c) trapezium
(a) Any arrangement of two copies whose outline is a parallelogram is correct. For example, two triangles sharing the vertical side, the second rotated half a turn about the middle of that side, with outline \((0, 0)\), \((4, 0)\), \((0, 7)\), \((-4, 7)\). Others: a half turn about the middle of the horizontal side, with outline \((0, 7)\), \((0, 0)\), \((4, -7)\), \((4, 0)\); or two copies joined along their hypotenuse to make the \(4\) by \(7\) rectangle \((0, 0)\), \((4, 0)\), \((4, 7)\), \((0, 7)\).
(b) Any arrangement of three copies whose outline is a trapezium is correct. For example, take the parallelogram from part (a) and add a third triangle with corners \((-4, 0)\), \((0, 0)\), \((-4, 7)\), giving the outline \((-4, 0)\), \((4, 0)\), \((0, 7)\), \((-4, 7)\). Another: add a third triangle with corners \((0, 0)\), \((0, -7)\), \((4, -7)\) to the half-turn parallelogram \((0, 7)\), \((0, 0)\), \((4, -7)\), \((4, 0)\), giving the outline \((0, 7)\), \((0, -7)\), \((4, -7)\), \((4, 0)\), whose vertical parallel sides are \(14\) and \(7\) squares long.
(c) Four triangles with their right angles meeting at one point, each a reflection of the next. Taking that point as the origin, the outline has vertices \((4, 0)\), \((0, 7)\), \((-4, 0)\) and \((0, -7)\).
rhombus
Any shading of 10 squares that leaves the grid with exactly two lines of symmetry
C(4, 5) and D(7, 5), with A, B, C, D joined in order (or, on the other side of AB, C(4, 1) and D(7, 1))
Also right:

discia.org Shapes · sheet 1