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.

  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 dimeter

    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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Updated: 14 March 2009 (A Dendane)


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