Grade 4 Geometry Questions and Problems With Solutions and Explanations

Solutions and explanations to Grade 4 geometry problems are presented.

  1. True or False: Two parallel lines intersect.
    Solution
    False: Two parallel lines do not intersect.

  2. A triangle is a closed planar shape with
    Solution
    3 sides. (tri in the word triangle means three, from Latin)

  3. A closed planar shape with 5 sides is called a
    Solution
    pentagon. (penta in the word pentagon means five, from Greek)

  4. A closed planar shape with 4 sides is called a
    Solution
    quadrilateral. (quadri in the word quadrilateral means four, from Latin)

  5. A line segment is defined by
    Solution
    2 points

  6. An equilateral triangle has
    Solution
    all three sides equal and all three angles equal.

  7. Which of the statements below best describes a square?

    Solution
    A square has 4 equal sides and 4 right angles.

  8. Which pair of lines are parallel?

    geometry, question 8


    Solution
    The pair of lines in A are parallel because they do not intersect.

  9. Which of these shapes are
    1. quadrilaterals?
    2. triangles?
    3. squares?

    geometry, question 9


    Solution
    i) quadrilaterals have 4 sides: shapes B, E F.
    ii) triangles have 3 sides: shapes A, D.
    iii) squares have 4 equal sides and 4 right angles: shape F.

  10. Which of these shapes are
    1. right triangles?
    2. rectangles?

    geometry, question 10


    Solution
    i) right triangles have 1 right angle: shape B.
    ii) rectangles have 2 pairs of parallel sides and 4 right angles: shapes D and E.

  11. Which pair of lines are
    1. parallel?
    2. perpendicular?

    geometry, question 11


    Solution
    i) parallel lines do not intersect. Lines S and R are parallel
    ii) perpendicular lines intersect and form a right angle (90 degrees). T and S , and T and R are pairs of perpendicular lines.

  12. Find the perimeter and area of each shape.

    geometry, question 12


    Solution
    Shape A
    Perimeter = 5 + 5 + 5 + 5 = 20
    Area = 5 5 = 25
    Shape B
    Perimeter = 9 + 6 + 9 + 6 = 30
    Area = 9 6 = 54
    Shape C
    Perimeter = 10 + 2 + 10 + 2 = 24
    Area = 10 2 = 20
    Shape D
    Perimeter = 5 + 4 + 5 + 4 = 18
    Area = 5 4 = 20

  13. Find the perimeter and area of each shape.

    geometry, question 13


    Solution
    Shape A: Perimeter is obtained by adding all sides. Starting from the top side we have
    Perimeter = 4 + 4 + 4 + 4 + 8 + 8 = 32
    Shape A: The area of the given shape is equal to the area of the square of side 8 from which the area of the small square top right of side 4 is subtracted.
    Area = 8 8 - 4 4 = 64 - 16 = 48
    Shape B: Perimeter is obtained by adding all sides. Starting from the top side we have
    Perimeter = 8 + 2 + 4 + 4 + 4 + 2 + 8 + 8 = 40
    Shape B: The area of the given shape is equal to the area of the square (left side) of side 8 to which the area of the small square (right side) of side 4 is added.
    Area = 8 8 + 4 4 = 64 + 16 = 80

  14. Which of these is an isosceles triangle?

    geometry, question 14


    Solution
    An isosceles triangle has two equal sides: shape B

  15. Which pair of triangles are congruent?

    geometry, question 15


    Solution
    Congruent shapes have sides of equal length: shapes A and C

  16. Point O is the center of the circle below. What do you call the segments
    1. AB?
    2. CD?
    3. OD?

    geometry, question 16


    Solution
    A segment whose endpoints are on a circle is called a chord: AB is a chord
    A chord that passes through the center of circle is called a diameter: CD is a diameter
    A segment whose 2 endpoints are: 1) the center of circle and 2) one point on the circle is called the radius: OD is a radius

Primary Maths (grades 4 and 5) with Free Questions and Problems With Answers
Middle School Maths (grades 6,7,8 and 9) with Free Questions and Problems With Answers
High School Maths (Grades 10, 11 and 12) - Free Questions and Problems With Answers
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