# 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

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?

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

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

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?

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?

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.

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.

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?

Solution
An isosceles triangle has two equal sides: shape B

15. Which pair of triangles are congruent?

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?

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