MATHEMATICS - PYTHAGOREAN THEOREM

Pythagorean Theorem Worksheet

10 questions
Know and use Pythagoras’ theorem.
Difficulty: Hard
Board: CAIE
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Here are the first 3 questions. Click “View all questions” to see the complete assessment.

Q1.
A rectangular courtyard has length $24\text{ m}$ and diagonal $26\text{ m}$ . What is its perimeter?

A) $70\text{ m}$
B) $60\text{ m}$
C) $68\text{ m}$
D) $52\text{ m}$

Q2.
A $17\text{ m}$ ladder rests against a vertical wall. Initially, its foot is $8\text{ m}$ from the wall. The foot is then moved so that it is $15\text{ m}$ from the wall. By how far does the top of the ladder move down the wall?

A) $6\text{ m}$
B) $9\text{ m}$
C) $7\text{ m}$
D) $8\text{ m}$

Q3.
The points $P(-4,2)$ and $Q(8,7)$ are plotted on a coordinate grid. What is the distance $PQ$ ?

A) $13$
B) $\sqrt{119}$
C) $17$
D) $12$

Q4.
An isosceles triangle has two equal sides of length $25\text{ cm}$ and a base of length $14\text{ cm}$ . What is its area?

A) $168\text{ cm}^2$
B) $84\text{ cm}^2$
C) $175\text{ cm}^2$
D) $336\text{ cm}^2$

Q5.
A vertical mast is supported by a cable from its top to an anchor $7\text{ m}$ from its base. This cable is $25\text{ m}$ long. A second cable runs from the same top to an anchor $10\text{ m}$ from the base. How long is the second cable?

A) $25\text{ m}$
B) $34\text{ m}$
C) $26\text{ m}$
D) $24\text{ m}$

Q6.
The perpendicular diagonals of a rhombus have lengths $16\text{ cm}$ and $30\text{ cm}$ . The diagonals bisect each other. What is the perimeter of the rhombus?

A) $64\text{ cm}$
B) $68\text{ cm}$
C) $92\text{ cm}$
D) $34\text{ cm}$

Q7.
A cuboid has length $24\text{ cm}$ , width $8\text{ cm}$ , and height $6\text{ cm}$ . What is the length of the straight line joining two opposite vertices of the cuboid?

A) $25\text{ cm}$
B) $26\text{ cm}$
C) $38\text{ cm}$
D) $28\text{ cm}$

Q8.
Use the measurements and right-angle marks in the figure to find $x$ .

Diagram for question 8: Use the measurements and right-angle marks in the figure to find x.

A) $6\text{ cm}$
B) $8\text{ cm}$
C) $10\text{ cm}$
D) $12\text{ cm}$

Q9.
What is the perimeter of trapezium $ABCD$ shown in the figure?

Diagram for question 9: What is the perimeter of trapezium ABCD shown in the figure?

A) $58\text{ cm}$
B) $66\text{ cm}$
C) $62\text{ cm}$
D) $70\text{ cm}$

Q10.
The figure shows a square. What is its area?

Diagram for question 10: The figure shows a square. What is its area?

A) $324\text{ cm}^2$
B) $162\text{ cm}^2$
C) $36\sqrt{2}\text{ cm}^2$
D) $81\text{ cm}^2$

What this assessment covers

Concepts Tested

pythagorean theorem
Know and use Pythagoras’ theorem.

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Hard questions included

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Assessment details

Total questions:: 10
Subject:: Mathematics
Topic:: Pythagorean Theorem
Difficulty:: Hard
Grade:: Grade 6
Board:: CAIE
Marks:: 10.00

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Q1. A rectangular courtyard has length 24 m and diagonal 26 m. What is its perimeter?

Q2. A 17 m ladder rests against a vertical wall. Initially, its foot is 8 m from the wall. The foot is then moved so that it is 15 m from the wall. By how far does the top of the ladder move down the wall?

Q3. The points P( − 4,2) and Q(8,7) are plotted on a coordinate grid. What is the distance PQ?

Q4. An isosceles triangle has two equal sides of length 25 cm and a base of length 14 cm. What is its area?

Q5. A vertical mast is supported by a cable from its top to an anchor 7 m from its base. This cable is 25 m long. A second cable runs from the same top to an anchor 10 m from the base. How long is the second cable?

Q6. The perpendicular diagonals of a rhombus have lengths 16 cm and 30 cm. The diagonals bisect each other. What is the perimeter of the rhombus?

Q7. A cuboid has length 24 cm, width 8 cm, and height 6 cm. What is the length of the straight line joining two opposite vertices of the cuboid?

Q8. Use the measurements and right-angle marks in the figure to find x.

Q9. What is the perimeter of trapezium ABCD shown in the figure?

Q10. The figure shows a square. What is its area?