Grade 4 Geometry Questions and Problems With Solutions and Explanations

Solutions and explanations to Grade 4 geometry problems are presented.

Questions and Problems with Their Solutions

  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

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