Grade 6 Geometry Practice — Easy

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Question 1 of 24: The area of a triangle formula is:

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Answer key for parents & teachers (24 questions)
  1. The area of a triangle formula is: — A = ½ × b × h. A triangle is half a parallelogram: A = ½ × base × height.
  2. The HEIGHT of a triangle is: — The perpendicular distance from the base to the opposite vertex. Height is always PERPENDICULAR to the base — it forms a 90° angle. It is NOT the slant side.
  3. A triangle has base 8 cm and height 5 cm. Area = ? — 20 cm². A = ½ × 8 × 5 = ½ × 40 = 20 cm².
  4. A triangle has base 12 in and height 6 in. Area = ? — 36 in². A = ½ × 12 × 6 = ½ × 72 = 36 in².
  5. How do you find the area of a COMPOSITE figure? — Decompose into simpler shapes, find each area, then add (or subtract). Decompose into rectangles, triangles, etc., find each area, then ADD or SUBTRACT to get the total.
  6. For an L-shaped figure: top part is 6×4=24 m², bottom part is 3×5=15 m². Total area = ? — 39 m². 24 + 15 = 39 m².
  7. A right triangle has legs 3 and 4. Area = ? — 6 sq units. A = ½ × base × height = ½ × 3 × 4 = 6 sq units.
  8. If a triangle has the same base and height as a rectangle, the triangle's area is: — Half the rectangle. A rectangle = b × h. A triangle = ½ × b × h. The triangle is HALF the rectangle with the same base and height.
  9. V = l × w × h works for rectangular prisms even when dimensions are: — Fractions or mixed numbers too. The formula V = l × w × h applies to any rectangular prism — regardless of whether dimensions are whole numbers, fractions, or decimals.
  10. Before multiplying mixed-number dimensions, you should: — Convert mixed numbers to improper fractions. Convert mixed numbers to improper fractions first (e.g., 2½ → 5/2) before multiplying. This avoids errors.
  11. What is ½ × ½ × ½? — 1/8. ½ × ½ = ¼, then ¼ × ½ = 1/8.
  12. A box: l=½, w=¾, h=1. Volume = ? — 3/8. V = ½ × ¾ × 1 = 3/8 cubic units.
  13. Volume is measured in: — Cubic units (³). Volume occupies 3D space and is always measured in cubic units (cm³, m³, in³, etc.).
  14. Convert 1½ to an improper fraction for multiplication. — 3/2. 1½ = (1×2+1)/2 = 3/2.
  15. A prism: l=2½, w=2, h=1½. First step: — Convert 2½ to 5/2 and 1½ to 3/2 first. Convert mixed numbers FIRST: 2½ = 5/2; 1½ = 3/2. Then V = 5/2 × 2 × 3/2.
  16. V = 5/2 × 2 × 3/2 = ? — 7.5. (5×2×3)/(2×1×2) = 30/4 = 7.5 = 7½ cubic units.
  17. Surface area is measured in: — Square units (²). Surface area covers the faces (flat 2D surfaces), so it is measured in SQUARE units (cm², m², in², etc.).
  18. A NET is: — A 2D pattern that folds up into a 3D shape. A NET is a 2D flat pattern that, when folded, creates a 3D solid. Finding the area of the net gives the surface area.
  19. A rectangular prism has how many FACES? — 6. A rectangular prism (box) has 6 faces: top, bottom, front, back, left, right.
  20. For a rectangular prism, the top and bottom faces have area: — l × w. Top and bottom faces are l × w rectangles.
  21. SA formula for a rectangular prism is: — SA = 2(lw + lh + wh). SA = 2(lw) + 2(lh) + 2(wh) = 2(lw + lh + wh). Each pair of opposite faces counted twice.
  22. A cube with side 3 cm. SA = ? — 54 cm². Each face = 3×3 = 9 cm². 6 faces: SA = 6×9 = 54 cm².
  23. A box: l=5, w=3, h=2. SA = 2(lw+lh+wh) = ? — 62. lw=15, lh=10, wh=6. SA=2(15+10+6)=2(31)=62 sq units.
  24. Why do we multiply each pair of faces by 2 in the SA formula? — Because opposite faces are congruent (identical pairs). A rectangular prism has 3 pairs of congruent opposite faces. Each pair contributes 2× the single face area.