Grade 4 Geometry Questions and Problems With Answers

Grade 4 geometry questions and problems are presented with detailed step-by-step solutions and explanations. There are 1 "true/false" question, 6 multiple choice questions, and other types of questions covering shapes, lines, perimeter, area, and circles.

Questions and Step-by-Step Solutions

  1. Question 1: True or False: Two parallel lines intersect.

    ► Solution to Question 1

    False: Two parallel lines do not intersect.

  2. Question 2: A triangle is a closed planar shape with

    1. 2 sides
    2. 4 sides
    3. 3 sides
    4. 5 sides
    ► Solution to Question 2

    A triangle has 3 sides (tri in the word triangle means three, from Latin).

    Therefore, option C is correct.

  3. Question 3: A closed planar shape with 5 sides is called a

    1. pentagon
    2. hexagon
    3. square
    4. heptagon
    ► Solution to Question 3

    A 5-sided shape is a pentagon (penta in the word pentagon means five, from Greek).

    Therefore, option A is correct.

  4. Question 4: A closed planar shape with 4 sides is called a

    1. segment
    2. hexagon
    3. quadrilateral
    4. heptagon
    ► Solution to Question 4

    A 4-sided shape is a quadrilateral (quadri in the word quadrilateral means four, from Latin).

    Therefore, option C is correct.

  5. Question 5: A line segment is defined by

    1. 1 point
    2. 3 points
    3. 2 points
    4. 4 points
    ► Solution to Question 5

    A line segment is a part of a line that has two distinct endpoints, so it is defined by 2 points.

    Therefore, option C is correct.

  6. Question 6: An equilateral triangle has

    1. only 2 equal sides
    2. all 3 sides equal
    3. no equal sides
    4. one right angle
    ► Solution to Question 6

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

    Therefore, option B is correct.

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

    1. A square has 4 equal sides and 4 right angles.
    2. A square has 4 equal sides.
    3. A square has 4 right angles.
    4. 2 pairs of parallel sides.
    ► Solution to Question 7

    A square has 4 equal sides and 4 right angles. This is the most precise and complete definition among the choices.

    Therefore, option A is correct.

  8. Question 8: Which pair of lines are parallel?

    geometry, question 8

    ► Solution to Question 8

    The pair of lines in A are parallel because they run side-by-side and do not intersect.

  9. Question 9: Which of these shapes are
    i) quadrilaterals?
    ii) triangles?
    iii) squares?

    geometry, question 9

    ► Solution to Question 9

    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. Question 10: Which of these shapes are
    i) right triangles?
    ii) rectangles?

    geometry, question 10

    ► Solution to Question 10

    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. Question 11: Which pair of lines are
    i) parallel?
    ii) perpendicular?

    geometry, question 11

    ► Solution to Question 11

    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. Question 12: Find the perimeter and area of each shape.

    geometry, question 12

    ► Solution to Question 12

    Shape A:
    Perimeter = \(5 + 5 + 5 + 5 = 20\)
    Area = \(5 \times 5 = 25\)

    Shape B:
    Perimeter = \(9 + 6 + 9 + 6 = 30\)
    Area = \(9 \times 6 = 54\)

    Shape C:
    Perimeter = \(10 + 2 + 10 + 2 = 24\)
    Area = \(10 \times 2 = 20\)

    Shape D:
    Perimeter = \(5 + 4 + 5 + 4 = 18\)
    Area = \(5 \times 4 = 20\)

  13. Question 13: Find the perimeter and area of each shape.

    geometry, question 13

    ► Solution to Question 13

    Shape A:
    Perimeter is obtained by adding all outer sides starting from the top side:
    Perimeter = \(4 + 4 + 4 + 4 + 8 + 8 = 32\)
    Area is equal to the area of the large square of side 8 minus the area of the small top-right square of side 4:
    Area = \(8 \times 8 - 4 \times 4 = 64 - 16 = 48\)

    Shape B:
    Perimeter is obtained by adding all outer sides:
    Perimeter = \(8 + 2 + 4 + 4 + 4 + 2 + 8 + 8 = 40\)
    Area is equal to the area of the square on the left of side 8 plus the area of the small square on the right of side 4:
    Area = \(8 \times 8 + 4 \times 4 = 64 + 16 = 80\)

  14. Question 14: Which of these is an isosceles triangle?

    geometry, question 14

    ► Solution to Question 14

    An isosceles triangle has two equal sides: shape B.

  15. Question 15: Which pair of triangles are congruent?

    geometry, question 15

    ► Solution to Question 15

    Congruent shapes have identical shapes and sides of equal length: shapes A and C.

  16. Question 16: Point O is the center of the circle below. What do you call the segments
    i) AB?
    ii) CD?
    iii) OD?

    geometry, question 16

    ► Solution to Question 16

    i) AB: A segment whose endpoints are on a circle is called a chord, so AB is a chord.
    ii) CD: A chord that passes through the center of a circle is called a diameter, so CD is a diameter.
    iii) OD: A segment with one endpoint at the center and the other on the circle is called a radius, so OD is a radius.

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