Grade 6 Geometry Practice — Medium

Question 1 of 22Score 0/0Medium

Question 1 of 22: A triangle has area 30 cm² and base 10 cm. What is its height?

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Answer key for parents & teachers (22 questions)
  1. A triangle has area 30 cm² and base 10 cm. What is its height? — 6 cm. 30 = ½ × 10 × h = 5h → h = 6 cm.
  2. A triangle has area 45 in² and height 9 in. What is its base? — 10 in. 45 = ½ × b × 9 = 4.5b → b = 45/4.5 = 10 in.
  3. An L-shaped room: overall rectangle is 10×8=80 m², minus a corner 4×3=12 m². Area = ? — 68 m². 80 − 12 = 68 m². Subtracting the missing corner from the full rectangle.
  4. A shape is a rectangle (6×8) with a triangle on top (base 6, height 4). Total area = ? — 60 sq units. Rectangle: 6×8=48. Triangle: ½×6×4=12. Total: 48+12=60 sq units.
  5. Two congruent triangles can be combined to form a: — Parallelogram. Two congruent triangles, placed base-to-base, form a PARALLELOGRAM (or rectangle). This is why A_triangle = ½ × A_parallelogram.
  6. For an obtuse triangle, the height drawn outside the triangle is still: — Perpendicular to the base (or base extended). Even for obtuse triangles, height is PERPENDICULAR to the base. For obtuse triangles, this often means the height falls outside the triangle, drawn to the base EXTENDED.
  7. A triangle with base 7 m and height 10 m has the same area as a rectangle with length 7 m and width: — 5 m. Triangle area = ½×7×10=35. Rectangle: 7×w=35 → w=5 m.
  8. A floor plan is 12×10 m with a triangular indentation removed: base 4, height 3. Area remaining? — 114 m². Rectangle: 12×10=120. Triangle removed: ½×4×3=6. Remaining: 120−6=114 m².
  9. A box: l=3/4, w=2/3, h=8. Volume = ? — 4. 3/4 × 2/3 = 6/12 = 1/2. Then 1/2 × 8 = 4 cubic units.
  10. A box: l=1½, w=1½, h=1½. Volume = ? — 3⅜. 3/2 × 3/2 × 3/2 = 27/8 = 3⅜ cubic units.
  11. A fish tank: l=2¼ ft, w=1½ ft, h=1⅓ ft. Volume = ? — 4½ ft³. 9/4 × 3/2 × 4/3 = (9×3×4)/(4×2×3) = 108/24 = 4½ ft³.
  12. If you fill a box (l=½, w=½, h=½) with ½-unit cubes, how many cubes fit? — 1. Only 1 cube fits — the box IS a ½-unit cube. V = (½)³ = 1/8 cubic units, and the cube volume is also 1/8.
  13. Volume = 7½ cm³ and base area = 2½ cm². Height = ? — 3 cm. V = B × h → 7½ = 2½ × h → h = (15/2)/(5/2) = 15/2 × 2/5 = 3 cm.
  14. What is the estimate for (2½ × 1½ × 3) before computing exactly? — ≈ 9 (using 3×1×3). Round: 2½≈3, 1½≈2, 3=3. Rough estimate: 3×2×3=18. But rounding 2½ up and 1½ up makes the estimate high. The exact is 11¼. Using 2×1×3=6 is low, 3×2×3=18 is high.
  15. A container holds exactly 1 m³. A brick measures ½m × ¼m × ⅓m. Volume of one brick = ? — 1/24 m³. ½ × ¼ × ⅓ = 1/24 m³.
  16. A box: l=8, w=6, h=4. SA = ? — 208 sq units. lw=48, lh=32, wh=24. SA=2(48+32+24)=2(104)=208.
  17. A cube has SA = 150 cm². What is the side length? — 5 cm. SA = 6s². 150 = 6s² → s² = 25 → s = 5 cm.
  18. What is the SA of a rectangular prism with l=10, w=4, h=3? — 164 sq units. lw=40, lh=30, wh=12. SA=2(40+30+12)=2(82)=164.
  19. An open box (no top) with l=6, w=4, h=2. SA = ? — 64 sq units. Full SA = 2(24+12+8) = 88. Subtract top: 88 − 6×4 = 88 − 24 = 64 sq units.
  20. A triangular prism has 2 triangular faces and 3 rectangular faces. Total faces = ? — 5. 2 triangular + 3 rectangular = 5 faces total.
  21. To find SA from a net, you: — Add all the face areas. From a net, find the area of each face and ADD them all together.
  22. A box wraps a gift. The box is 20×15×10 cm. How much wrapping paper (minimum)? — 1,300 cm². SA = 2(300+200+150) = 2(650) = 1,300 cm².