*This Math quiz is called 'Perimeter and Area 3' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.*

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Area is the size of the surface of a two-dimensional (2D) or three-dimensional (3D) shape. The area of a three-dimensional shape is worked out by adding the area of each of its faces together. The area of each of its faces is worked out in the same way as the area of 2D shapes. This Perimeter and Area quiz is all about the perimeter and area of 2D shapes and the surface area of 3D shapes.

1.

What is the formula for calculating the area of a rectangle?

2 x length x 2 x width

2 x length + 2 x width

Length + width

Length x width

2.

1cm^{2} is equivalent to how many mm^{2}?

1mm^{2}

10mm^{2}

100mm^{2}

1,000mm^{2}

There are 10mm in a cm so 10 x 10 = 100

3.

A regular heptagon has a perimeter of 63cm. What length is each side?

6.3cm

9cm

10cm

12cm

A regular heptagon has 7 equal sides. To find the length of each side divide the perimeter by 7

4.

What is the perimeter of a regular octagon with sides of 12cm?

20cm

56cm

96cm

160cm

Octagons have 8 sides so 12 x 8 = 96

5.

How do we calculate the area of a right angled triangle?

Length x width then halve

Length + width then double

Length x width then double

Length x width then quarter

Right angled triangles are rectangles cut in half so the formula is the same as for a rectangle but then halved

6.

What is the surface area of a cuboid with measurements of 4cm x 5cm x 6cm?

74cm^{2}

100cm^{2}

148cm^{2}

174cm^{2}

2 of the faces will be 4cm x 5cm = 20cm^{2}

2 of the faces will be 4cm x 6cm = 24cm^{2}

2 of the faces will be 5cm x 6cm = 30 cm^{2}

20 + 20 + 24 + 24 + 30 + 30 = 148

2 of the faces will be 4cm x 6cm = 24cm

2 of the faces will be 5cm x 6cm = 30 cm

20 + 20 + 24 + 24 + 30 + 30 = 148

7.

What is the perimeter of a regular decagon with sides of 23cm?

46cm

115cm

200cm

230cm

A regular decagon has 10 equal sides, so we multiply the length of the side by 10 to calculate the perimeter

8.

What is the surface area of a cube with sides of 5cm?

25cm^{2}

75cm^{2}

125cm^{2}

150cm^{2}

The area of each face is 25cm^{2}. There are 6 faces, so multiply 25cm^{2} by 6 to give 150cm^{2}

9.

What is the area of a right angle triangle with width 12cm and length 6cm?

18cm^{2}

36cm^{2}

72cm^{2}

148cm^{2}

12 x 6 = 72

72 ÷ 2 = 36

72 ÷ 2 = 36

10.

How would you find the area of an L-shape?

Divide into rectangles; work out the areas of each and then divide one by the other

Divide into rectangles; work out the areas of each and then multiply one by the other

Divide into rectangles; work out the areas of each and then add together

Divide into rectangles; work out the areas of each and then subtract one from the other

Always simplify shapes if you can

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