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Compound Shapes Questions and Answers

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Question 16 - Bancrofts School 11 Plus Maths Sample Entrance Paper 2023

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Question 15 - Bancrofts School 11 Plus Maths Sample Entrance Paper 2023

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Question 14 - Bancrofts School 11 Plus Maths Sample Entrance Paper 2023

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Question 18 - Oundle School Second Form Mathematics 2021

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Question 10 Dulwich College Maths Speciment Paper J

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Question 35-Merchant Taylors School 11 Plus Maths Entrance Examination 2021

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Question 18-Latymer Upper School 11 Maths Sample Paper 1 2021

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Compound Shapes for the 11 Plus Entrance Exam

1. What are Compound Shapes?

A compound shape is made up of two or more basic shapes joined together. The basic shapes are squares, rectangles, triangles etc. The compound shape below is made up of a square and a triangle.

11+ Topicwise Compound Shapes Article image 1

1.1 How to find the Area of Compound Shapes?

To find the area of compound shapes, divide the compound shape into smaller shapes, then find the area of each of the smaller shapes and add them. Our final answer must be in square units e.g. m², cm², in² or ft², etc.

For example,

11+ Topicwise Compound Shapes Article image 2

The compound shape is made up of rectangle A and square B.

Area of Compound Shape = Area of Rectangle A + Area of Square B

1.2 How to find the Perimeter of Compound Shapes?

The perimeter of a shape is the total distance around its edge. To calculate the perimeter of a shape, you just have to add up the lengths of all of its sides. In Compound shapes, the lengths of some of the sides may be missing. To work out the missing lengths we can use the other side lengths. Let’s learn this with an example.

11+ Topicwise Compound Shapes Article image 3

In the shape above to calculate the perimeter, we need to know the two missing lengths.

The vertical length will be 9 cm - 5 cm = 4 cm

The horizontal length will be 11 cm - 4 cm = 7 cm

11+ Topicwise Compound Shapes Article image 4

We can find the perimeter by adding the length of every side of the figure together:

Perimeter = 9 + 4 + 4 + 7 + 5 + 11 = 40 cm

1.3 Examples on Compound Shapes

Example: Find the area and the perimeter of the compound shape below.

11+ Topicwise Compound Shapes Article image 5

Solution: Let’s split the shape into two rectangles and find the missing lengths.

11+ Topicwise Compound Shapes Article image 6

Perimeter = 4 + 6 + 6 + 3 + 10 + 9 = 38 cm

Area of rectangle = length × width

Area of rectangle A = 4 × 6 = 24 cm²

Area of rectangle B = 10 × 3 = 30 cm²

Area of compound shape = Area of rectangle A + Area of rectangle B

Area of compound shape = 24 + 30= 54 cm²

Example: Work out the area of the compound shape given below.

11+ Topicwise Compound Shapes Article image 7

Solution: Let’s split the shape into a rectangle and a trapezium.

11+ Topicwise Compound Shapes Article image 8

Area of rectangle A = length × width

                                 = 10 × 6

                                 = 60 in²

Area of trapezium B = 1⁄2 × (sum of parallel sides) ×  height

Height of trapezium = 12 - 6 = 6 in

Area of trapezium B = 1⁄2 × (8 + 10) × 6

                                  = 18⁄2 × 6

                                  = 9 × 6

                                  = 54 in²

Area of compound shape = Area of rectangle A + Area of trapezium B

                                         = 60 + 54

                                         = 114 in²

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  • Frequently Asked Questions
    What is a good score in 11+ Maths ?

    What counts as a "good" score will vary depending on the school you want to attend. The standardized 11 Plus test score average across the country is roughly 100. The highest average in some areas is 111. The lowest scores would often fall between 60 and 70, while the highest scores would normally fall between 130 and 140. To achieve excellent marks on 11+ Maths Exams, practice 11+ Maths topic-wise questions.

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    The best way to prepare for the 11+ Maths Exam is by practicing 11+ Maths topic-wise questions regularly.

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    What do you need to know for the 11 Plus Maths exam?

    The children must master the following topics for the 11 plus exams

    • Number and place value.
    • Addition, subtraction, multiplication, and division.
    • Fractions, percentages, decimals.
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    • Measurement.
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