3rd Grade Quadrilaterals and Partitioning Shapes Worksheet Solutions (PDF)
This quadrilaterals practice solutions for 3rd Grade covers quadrilaterals and partitioning shapes (Common Core 3.G.A.1, 3.G.A.2), with a free PDF to print.
Every problem has a full worked solution and the final answer in bold. Check each shape by counting sides and right angles, and check each partition by comparing areas. Use this key to find mistakes with attributes and unit fractions.
Grade 3 · Common Core State Standards: 3.G.A.1, 3.G.A.2
Quadrilaterals practice solutions: exercises 1 to 10
Exercise 1 – Sides and corners
“Quad” means four. A quadrilateral has 4 sides and 4 corners.
Exercise 2 – Find the quadrilaterals
Count the sides of each shape. A has 5 sides and C has 3 sides, so they are not quadrilaterals. B, D, E, and F each have 4 sides.
B, D, E, F
Exercise 3 – Mystery shape one
4 equal sides and 4 right angles describe a square.
Square
Exercise 4 – Right angles in a rectangle
All 4 corners of a rectangle are square corners.
4 right angles
Exercise 5 – Name the tick-mark shape
All 4 sides have a tick mark, so they are equal. A quadrilateral with 4 equal sides and no right angles is a rhombus.
Rhombus
Exercise 6 – Square and rectangle
A rectangle is a quadrilateral with 4 right angles. Every square has 4 right angles.
True
Exercise 7 – Rhombus and square
A rhombus has 4 equal sides, but its corners do not have to be right angles. A rhombus that leans over has no right angles, so it is not a square.
False
Exercise 8 – Mystery shape two
4 right angles make it a rectangle. The sides are not all equal, so it is not a square.
Rectangle
Exercise 9 – Draw a different quadrilateral
Join 4 points with straight sides so that the sides are not all equal and there are no 4 right angles. A kite works. Many other drawings are correct too.
Exercise 10 – A shared attribute
Each one has 4 sides, so each is a quadrilateral. Each one also has two pairs of parallel sides. Either answer is correct.
4 sides (or 2 pairs of parallel sides)
Exercises 11 and up
Exercise 11 – Rhombus but not square
G has unequal sides. I has only one pair of parallel sides. J is a square. H has 4 equal sides and no right angles.
H
Exercise 12 – Complete the table
| Shape | 4 equal sides? | 4 right angles? |
|---|---|---|
| Square | yes | yes |
| Rectangle that is not a square | no | yes |
| Rhombus that is not a square | yes | no |
A rectangle that is not a square has long and short sides. A rhombus is not required to have right angles.
Exercise 13 – Fix the claim
Having 4 sides only makes a shape a quadrilateral. A rectangle must also have 4 right angles. A trapezoid has just one pair of parallel sides and does not have 4 right angles.
4 sides is not enough to be a rectangle.
Exercise 14 – One part of six
One of 6 equal parts is 1 over 6.
\(\frac{1}{6}\)
Exercise 15 – Shaded part
There are 4 equal parts and 1 is shaded.
\(\frac{1}{4}\)
Exercise 16 – Is it a third?
One third of 12 squares is \(12 \div 3 = 4\) squares. The shaded part has 5 squares, which is more than 4.
No
Exercise 17 – Cracker pieces
The cracker is cut into 8 equal parts, so each part is 1 over 8.
\(\frac{1}{8}\)
Exercise 18 – Quilt block
4 triangles with equal area means each is 1 over 4 of the block.
\(\frac{1}{4}\)
Exercise 19 – Brownie pan
6 equal pieces means each piece is 1 over 6 of the pan.
\(\frac{1}{6}\)
Exercise 20 – Two ways to halve
Cut 1 makes 2 triangles. Each has area \(200 \times 100 \div 2 = 10{,}000\) square units. Cut 2 makes 2 trapezoids. Each has area \((60 + 140) \div 2 \times 100 = 10{,}000\) square units. Both cuts make two parts with equal area, so each part is \(\frac{1}{2}\).
Yes, both cuts make halves.
Exercise 21 – Garden beds
\(12 \div 3 = 4\), so each bed has 4 squares. Each bed is 1 of 3 equal parts.
4 squares; \(\frac{1}{3}\) of the garden
Exercise 22 – Cut the shape
4 equal sides and 4 right angles make a square. Four equal parts are fourths. Cutting down the middle both ways makes 4 small squares. Cutting along both diagonals makes 4 triangles.
Square; \(\frac{1}{4}\); small squares (or triangles)
Exercise 23 – Comparing pieces
Priya’s pieces are halves: \(\frac{1}{2}\). Jamal’s pieces are fourths: \(\frac{1}{4}\). The same napkin is shared by more pieces, so each piece is smaller.
Jamal’s pieces are smaller.
Exercise 24 – Folded strip
The strip has 5 equal parts, so the unit fraction uses 5 in the bottom. Carlos used 6, which is the wrong number of parts.
Each part is \(\frac{1}{5}\) of the strip.
Key facts behind this quadrilaterals practice solutions
- A quadrilateral has exactly 4 straight sides and 4 corners.
- A rhombus has 4 equal sides; a rectangle has 4 right angles.
- A square is a rhombus and a rectangle at the same time.
- Some quadrilaterals are not rhombuses, rectangles, or squares.
- Equal parts have equal area, and each of n equal parts is 1/n of the whole.
How to use this quadrilaterals practice solutions
Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.
Download the quadrilaterals practice solutions as a PDF with the button below and keep it with your notes.
Download the quadrilaterals practice solutions as a PDF with the button below and keep it with your notes.
Download the quadrilaterals practice solutions as a PDF with the button below and keep it with your notes.
All Grade 3 chapters: Grade 3 math.
