Grade 3 Geometry Practice — Medium

Question 1 of 24Score 0/0Medium

Question 1 of 24: A rhombus and a square both have 4 equal sides. What does a square have that a rhombus does NOT always have?

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Keep going: Read the lesson: Classifying Quadrilaterals
Answer key for parents & teachers (24 questions)
  1. A rhombus and a square both have 4 equal sides. What does a square have that a rhombus does NOT always have? — Right angles (90°). A square MUST have right angles. A rhombus has 4 equal sides but its angles can be acute or obtuse — not necessarily 90°.
  2. Which of these is NOT a quadrilateral? — Hexagon. A hexagon has 6 sides, not 4. All the others (trapezoid, rectangle, rhombus) are quadrilaterals with 4 sides.
  3. A shape has 2 pairs of parallel sides and all 4 sides are equal, but NO right angles. What is it? — Rhombus. This describes a rhombus — 4 equal sides, 2 pairs of parallel sides, but angles are not 90°.
  4. Every rectangle is a parallelogram. Is this true? — Yes, rectangles have 2 pairs of parallel sides. A parallelogram needs 2 pairs of parallel sides. Every rectangle has that, so rectangles are a special type of parallelogram.
  5. Which quadrilateral can have NO sides of equal length and NO parallel sides? — General quadrilateral. A general (irregular) quadrilateral just needs 4 sides — they don't have to be equal or parallel.
  6. A shape has vertices at (0,0), (4,0), (4,3), (0,3). What quadrilateral is it? — Rectangle. This shape has opposite sides equal (4 and 3 units) and all right angles — it's a rectangle.
  7. Which property do a square, rectangle, rhombus, and parallelogram ALL share? — 2 pairs of parallel sides. All four shapes are parallelograms — they all have 2 pairs of parallel sides.
  8. A trapezoid has angles of 60°, 120°, 60°, 120°. What is the sum of all its angles? — 360°. 60 + 120 + 60 + 120 = 360°. The sum of interior angles in ANY quadrilateral is always 360°.
  9. A rectangle is partitioned into 4 columns of equal width. Each column is what fraction of the rectangle? — 1/4. 4 equal columns means each column = 1/4 of the whole rectangle.
  10. You shade 5/8 of a shape. What fraction is NOT shaded? — 3/8. The whole = 8/8. Unshaded = 8/8 − 5/8 = 3/8.
  11. A square is split into 4 equal parts two different ways: by rows (2×2 grid) vs by triangles. Are both valid partitions? — Both are valid if parts have equal area. A partition is valid as long as parts have equal area — the shape of each part doesn't matter.
  12. A whole rectangle has area 24 sq cm. It's partitioned into 6 equal parts. What is the area of each part? — 4 sq cm. 24 Ãˇ 6 = 4 sq cm per part.
  13. Two students partition the same square differently — one into 4 parts, one into 8 parts. Both are correct. What does this tell us? — Shapes can be partitioned in multiple ways. The same shape can be validly partitioned into different numbers of equal parts. More parts = smaller fractions.
  14. A shape is partitioned into 3 equal parts. Each part equals what fraction of the whole? — 1/3. 3 equal parts → each part = 1 Ãˇ 3 = 1/3 of the whole.
  15. A rectangle partitioned into 4 parts: 2 parts are shaded. What is the simplest fraction of the shaded area? — 1/2. 2 out of 4 = 2/4 = 1/2. Both are correct, but 1/2 is the simplest form.
  16. A circle is cut into 8 equal parts. Anna shades 6 parts. Which fraction is NOT equivalent to the shaded area? — 2/3. 6/8 = 3/4 = 0.75. But 2/3 ≈ 0.667, which is different. So 2/3 is NOT equivalent.
  17. Two rectangles: A is 3×8 and B is 6×4. Which has the greater area? — They are equal. A = 3 × 8 = 24 sq units. B = 6 × 4 = 24 sq units. They have equal areas!
  18. A shape is made of a 4×5 rectangle on top of a 2×3 rectangle. What is the total area? — 26 sq units. 4 × 5 = 20; 2 × 3 = 6; 20 + 6 = 26 sq units total.
  19. A rectangle has an area of 36 sq units and a width of 4 units. What is its length? — 9 units. Area = l × w → 36 = l × 4 → l = 36 Ãˇ 4 = 9 units.
  20. An L-shaped room is split into two rectangles: 5×3 and 2×4. What is the total area of the room? — 23 sq units. 5 × 3 = 15; 2 × 4 = 8; 15 + 8 = 23 sq units.
  21. Rectangle A: 6×3 = 18 sq units. Rectangle B: 9×2 = 18 sq units. Which has a larger perimeter? — Rectangle A (18 units). P of A = 2(6+3) = 18 units. P of B = 2(9+2) = 22 units. B has the larger perimeter, not A. Wait — B is larger (22 > 18), so Rectangle B has the larger perimeter.
  22. A tile floor uses 1-foot square tiles. The room is 8 feet by 6 feet. How many tiles are needed? — 48. 8 × 6 = 48 tiles. Each tile covers 1 square foot, so you need 48 tiles.
  23. A shape has area 20 sq units. You add a 2×3 rectangle to it. What is the new total area? — 26 sq units. 2 × 3 = 6 sq units added; 20 + 6 = 26 sq units total.
  24. A rectangle is 10 units long. Its area is 70 sq units. How wide is it? — 7 units. Area = l × w → 70 = 10 × w → w = 70 Ãˇ 10 = 7 units.