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Trapezium: Challenge & Extension

Mathematics

GCSE Higher

14 questions

~28 mins

1 views0 downloads

About This Worksheet

A worksheet exploring the properties, calculations, and real-world applications of trapeziums, tailored for GCSE Higher students. It includes a range of questions from procedural practice to challenging extension problems.

Topics covered:

#Mathematics

#Geometry & Measures

#Properties of Quadrilaterals

#Trapezium

#GCSE Higher

Worksheet Preview

Full preview • 14 questions

Trapezium: Challenge & Extension

Subject: MathematicsGrade: GCSE Higher

Name:

Date:

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Untitled Worksheet

Grade GCSE Higher

Fluency & Practice

Answer all questions. Show your working in the grid spaces provided.

Calculate the length of the parallel side AB in a trapezium where the non-parallel sides are both 5 cm, the distance between the bases is 8 cm, and the height is 6 cm, given that the top base is 4 cm shorter than the bottom base.

[2 marks]

A trapezium has bases of lengths 12 cm and 20 cm, and its height is 9 cm. Calculate its area.

[3 marks]

In a trapezium, the lengths of the bases are 15 cm and 9 cm. The non-parallel sides are equal and measure 7 cm each. Find the measure of the angles at the bases.

[3 marks]

Construct a trapezium on the grid with a bottom base of 10 cm, a top base of 6 cm, and equal non-parallel sides. Label the vertices A, B, C, D clockwise starting at the bottom left.

[4 marks]

Problem Solving & Reasoning

Answer the following multi-step questions, showing your reasoning.

A trapezium has bases of 14 cm and 20 cm, with legs measuring 8 cm and 10 cm respectively. Is the trapezium isosceles? Justify your answer.

[3 marks]

Given a trapezium with bases 9 cm and 15 cm, and non-parallel sides 7 cm and 10 cm, calculate its height and area.

[4 marks]

Explain how the properties of a trapezium change if the non-parallel sides are unequal. Use diagrams or reasoning to support your answer.

[3 marks]

Construct a trapezium where the top base is twice the length of the bottom base, and the non-parallel sides are equal. Calculate the area when the bottom base is 8 cm and the height is 5 cm.

[4 marks]

Real-world Applications

Solve these contextual problems involving trapeziums.

A garden border is designed in the shape of a trapezium. The longer base is 12 meters, the shorter base is 8 meters, and the height is 3 meters. Calculate the amount of fencing needed to enclose the border.

[3 marks]

A roofing framework is in the shape of a trapezium with bases measuring 5 m and 3 m, and non-parallel sides measuring 4 m each. Find the total length of the framework.

[3 marks]

Challenge & Extension

Attempt these advanced problems for extension.

Prove that a trapezium with equal diagonals must be isosceles. Use geometric reasoning or coordinate geometry.

[4 marks]

Given a trapezium with bases 10 cm and 14 cm, and legs of 6 cm each, find the length of the diagonals and determine if the diagonals are equal.

[4 marks]

Mixed Review & Error Analysis

Answer the questions and identify common mistakes.

A student calculates the area of a trapezium with bases 9 cm and 13 cm, and height 4 cm, using the formula for rectangles. Explain what mistake they made and correct it.

[3 marks]

Construct a trapezium with bases 7 cm and 11 cm, and non-parallel sides of 5 cm and 8 cm. Calculate its area and discuss if the sides could be adjusted to make it isosceles.

[4 marks]

Answer Key

Fluency & Practice

Question 1: Calculate the length of the parallel side AB in a trapezium where the non-parallel sides are both 5 cm, the distance between the bases is 8 cm, and the height is 6 cm, given that the top base is 4 cm shorter than the bottom base.

Answer: 10

Question 2: A trapezium has bases of lengths 12 cm and 20 cm, and its height is 9 cm. Calculate its area.

Answer: 144

Question 3: In a trapezium, the lengths of the bases are 15 cm and 9 cm. The non-parallel sides are equal and measure 7 cm each. Find the measure of the angles at the bases.

Answer: angle1=60°, angle2=120°

Question 4: Construct a trapezium on the grid with a bottom base of 10 cm, a top base of 6 cm, and equal non-parallel sides. Label the vertices A, B, C, D clockwise starting at the bottom left.