Geometry — Practice

Question 1

How many sides and how many corners does a hexagon have?

Accepted Answer

Six sides and six corners. Every polygon has as many corners as it has sides, so counting one gives you the other.

Question 2

Name the polygon that has 5 sides, and say whether a circle is a polygon.

Accepted Answer

A five-sided polygon is a pentagon. A circle is not a polygon at all, because it has no straight sides and no corners.

Question 3

How many lines of symmetry does a square have, and how many does a rectangle have?

Accepted Answer

A square has four and a rectangle has two. The rectangle's two are the vertical fold and the horizontal fold through the middle.

Question 4

Find the perimeter of a rectangle that is 12 m long and 7 m wide.

Accepted Answer

Perimeter = 2 x (12 + 7) = 2 x 19 = 38 m. The answer is in metres, not square metres, because perimeter is a distance.

Question 5

A square has a side of 6 cm and a triangle has sides 7 cm, 8 cm and 9 cm. Find both perimeters and compare them.

Accepted Answer

Square: 4 x 6 = 24 cm. Triangle: 7 + 8 + 9 = 24 cm. Both are 24 cm, which shows that perimeter tells you the distance around and nothing about the shape.

Question 6

Which of these tessellate: circle, square, regular hexagon, regular pentagon?

Accepted Answer

The square and the regular hexagon tessellate. The circle leaves gaps because its edges are curved, and the regular pentagon leaves gaps however you turn it.

Question 7

How many faces, edges and vertices does a cube have, and how does a cuboid differ from it?

Accepted Answer

A cube has 6 faces, 12 edges and 8 vertices. A cuboid has exactly the same counts. The difference is that every face of a cube is a square, while a cuboid's faces are rectangles.

Question 8

A rectangular playground measures 30 m by 20 m. How far does a child walk in going around it twice?

Accepted Answer

One lap is the perimeter, 2 x (30 + 20) = 100 m. Two laps are 200 m.

Question 9

A classmate says the diagonal of a rectangle is a line of symmetry. Show that this is wrong.

Accepted Answer

Fold a rectangular sheet of paper along its diagonal. The two halves do not land on each other and the corners do not meet, so it is not a line of symmetry. A rectangle has only two: the vertical and the horizontal fold through the middle.

Question 10

Write the capital letters A, H and T. How many lines of symmetry does each have, and where do they lie?

Accepted Answer

A has one, straight down the middle. T has one, also straight down the middle. H has two: one down the middle and one across the middle.

Practice — Geometry

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