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Similar shapes (lengths)

Free Printable Similar shapes (lengths) PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 5)

Download free similar shapes (lengths) worksheets (PDF), GCSE maths past paper questions and worked solutions for Similar shapes (lengths) (5T). This is a Grade 5 geometry topic from the GCSE questions by topic collection for Foundation and Higher tier crossover GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Maths4Everyone, Corbett Maths, 1st Class Maths, Maths Made Easy, Dr Frost, Dr Austin, Metatutor, GCSE Maths Rocket, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our similar shapes (lengths) revision notes and worked examples with diagrams, try real GCSE past paper similar shapes (lengths) questions with step-by-step solutions, or download a PDF of all similar shapes (lengths) worksheet links.

Free Similar shapes (lengths) PDF Worksheets & Answers

Grade 5 • Topic 5T
Resource Questions Answers
GCSE past paper questions & solutions
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Graded exam questions & solutions
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GCSE 9–1 practice booklet & solutions
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Practice Questions & answers
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Grade 5 topics
5A - Combining ratios5B - Direct and inverse proportion
5C - Reverse percentages5D - Standard form
5E - Speed5F - Changing the subject
5G - Quadratic expressions5H - Solving quadratic equations
5J - Drawing quadratic graphs5K - Cubic/reciprocal graphs
5L - Simultaneous equations5M - Sector areas and arc lengths
5N - Sim. equ. graphically5P - Midpoint of a line segment
5Q - Gradient of a line5R - Equation of a line
5S - Spheres and cones5T - Similar shapes (lengths)
5U - Trigonometry (SOHCAHTOA)5V - Exact trig. values
5W - Probability trees5X - Vectors
5Y - Venn diagrams5Z - Density
5AA - Pressure
GCSE Maths Grade 5 Revision Notes & Method

Guide to Similar shapes (lengths): Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

Two shapes are mathematically similar if one is an enlargement of the other: corresponding angles are equal and corresponding sides are in the same ratio. First find the scale factor k = new lengthold length using two corresponding known sides.

Multiply by the scale factor to find a missing side on the larger shape, or divide by the scale factor to find a side on the smaller shape. When a smaller triangle is inside a larger triangle with parallel bases, sketch the two triangles separately using the full side length of the large triangle.

Example 1: Rectangles A and B are similar. Width of A is 6 cm and width of B is 15 cm. Length of B is 22.5 cm. Find the length of A.

Solution:

Scale factor k = 15 ÷ 6 = 2.5
Divide for smaller shape A:
Length A = 22.5 ÷ 2.5 = 9 cm
A B 6 ? cm 15 22.5 cm

Example 2: In ▵ABC, DE is parallel to BC (D on AB, E on AC). Given AD = 4 cm, DB = 6 cm and DE = 5 cm, find BC.

Solution:

Full AB = 4 + 6 = 10 cm
k = 10 ÷ 4 = 2.5
BC = 5 × 2.5 = 12.5 cm
A B C D E 4 6 5 cm BC = ?
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Similar shapes (lengths) Questions & Answers

Past Paper Example 1 IGCSE Nov 2021 2F Q20 / 2H Q4 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
ABC and DEF are similar triangles.
ABC45 cmDEF20 cm36 cmDiagram NOTaccurately drawn
(a) Work out the length of AB. [2 marks]
(b) work out the length of EF. [2 marks]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
Scale factor = 45 ÷ 20 = 2.25 M1
⇒ AB = 36 × 2.25 = 81 cm A1
Answer (a): 81 cm
Part (b) Solution:
EF = 54 ÷ 2.25 = 24 cm M1 A1
Answer (b): 24 cm
Past Paper Example 2 GCSE Jun 2017 2H Q5 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
ABCDE
ABC and EDC are straight lines. EA is parallel to DB. EC = 8.1 cm, DC = 5.4 cm, DB = 2.6 cm. (a) Work out the length of AE. (2) AC = 6.15 cm. (b) Work out the length of AB. (2)
ABC and EDC are straight lines.
EA is parallel to DB.
EC = 8.1 cm.
DC = 5.4 cm.
DB = 2.6 cm.
(a) Work out the length of AE. [2 marks]
(b) Work out the length of AB. [2 marks]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
Scale factor = 8.1 ÷ 5.4 = 1.5. AE = 2.6 × 1.5 = 3.9 cm M1 A1
Answer (a): 3.9 cm
Part (b) Solution:
BC = 6.15 ÷ 1.5 = 4.1 cm M1
AB = 6.15 – 4.1 = 2.05 cm A1
Answer (b): 2.05 cm
Past Paper Example 3 GCSE Jun 2017 2F Q21 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
ABCDE
Triangles ACE and BCD are similar. EC = 8.1 cm, DC = 5.4 cm, DB = 2.6 cm. (a) Work out AE. (2) (b) AC = 6.15 cm. Work out AB. (2)
ABC and EDC are straight lines.
EA is parallel to DB.
EC = 8.1 cm.
DC = 5.4 cm.
DB = 2.6 cm.
(a) Work out the length of AE. [2 marks]
(b) Work out the length of AB. [2 marks]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
Scale factor = 8.1 ÷ 5.4 = 1.5 M1
AE = 2.6 × 1.5 = 3.9 cm A1
Answer (a): 3.9 cm
Part (b) Solution:
BC = 6.15 ÷ 1.5 = 4.1 cm M1
AB = 6.15 – 4.1 = 2.05 cm A1
Answer (b): 2.05 cm

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