Solve Area and Volume Problems - 7th Grade Math

1. What is the volume formula for a right prism with base area $B$ and height $h$?

   $V=Bh$. Base area times height for any right prism.

2. What is the surface area of a right prism with $B=15$, $P=14$, and height $h=4$?

   $SA=86$. Apply $SA=2B+Ph$: $2(15) + 14(4) = 30 + 56 = 86$.

3. What is the area formula for a square with side length $s$?

   $A=s^2$. Square the side length for a square's area.

4. State the formula for the surface area of a right prism using perimeter $P$, height $h$, and base area $B$.

   $SA=Ph+2B$. Lateral area plus two base areas gives total surface area.

5. A box is $8$ by $5$ by $3$. What is its volume in cubic units?

   $120$. Volume equals $lwh$: $(8)(5)(3)=120$.

6. What is the surface area formula for a rectangular prism with dimensions $l,w,h$?

   $SA=2lw+2lh+2wh$. Sum of areas of all six rectangular faces.

7. State the formula for the circumference of a circle with radius $r$.

   $C=2\pi r$. Circumference equals twice pi times the radius.

8. State the formula for the area of a rectangle with length $l$ and width $w$.

   $A=lw$. Rectangle area equals length times width.

9. State the formula for the volume of a cube with side length $s$.

   $V=s^3$. Cube volume equals side length cubed.

10. State the formula for the area of a circle with radius $r$.

    $A=\pi r^2$. Circle area equals pi times radius squared.

11. State the formula for the area of a trapezoid with bases $b_1,b_2$ and height $h$.

    $A=\frac{1}{2}(b_1+b_2)h$. Trapezoid area uses average of parallel bases times height.

12. What is the volume of a right prism with base area $B=12$ and height $h=5$?

    $V=60$. Apply $V=Bh$: $12 \times 5 = 60$.

13. What is the area formula for a triangle with base $b$ and height $h$?

    $A=\frac{1}{2}bh$. Half the base times height gives the triangle's area.

14. What is the surface area of a right prism with $P=18$, $h=7$, and $B=20$?

    $166$. Using $SA=Ph+2B$: $(18)(7)+2(20)=126+40=166$.

15. State the formula for the area of a square with side length $s$.

    $A=s^2$. Square area equals side length squared.

16. What is the area formula for a rectangle with length $l$ and width $w$?

    $A=lw$. Multiply length by width for rectangular area.

17. Find the area of a square with side length $s=11$.

    $121$. Using $A=s^2$: $(11)^2=121$.

18. Find the surface area of a cube with side length $s=4$.

    $96$. Cube has 6 faces: $SA=6s^2=6(4)^2=96$.

19. What is the area formula for a trapezoid with bases $b_1,b_2$ and height $h$?

    $A=\frac{1}{2}(b_1+b_2)h$. Average of parallel bases times height.

20. What is the area of a rectangle with $l=9$ and $w=7$?

    $A=63$. Apply $A=lw$: $9 \times 7 = 63$.

21. Find the area of a rectangle with $l=7$ and $w=3$.

    $21$. Using $A=lw$: $(7)(3)=21$.

22. What is the surface area of a cube with side length $s=4$?

    $SA=96$. Apply $SA=6s^2$: $6 \times 4^2 = 6 \times 16 = 96$.

23. State the formula for the area of a triangle with base $b$ and height $h$.

    $A=\frac{1}{2}bh$. Triangle area equals half the base times height.

24. What is the base area $B$ of a rectangular prism base with $l=9$ and $w=4$?

    $36$. Base area equals $lw$: $(9)(4)=36$.

25. What is the area of a trapezoid with $b_1=8$, $b_2=14$, and $h=5$?

    $55$. Using trapezoid formula: $\frac{1}{2}(8+14)(5)=55$.

26. What is the volume formula for a cube with side length $s$?

    $V=s^3$. Cube the side length for volume.

27. State the formula for the area of a parallelogram with base $b$ and height $h$.

    $A=bh$. Parallelogram area equals base times perpendicular height.

28. A right prism has volume $V=96$ and base area $B=12$. What is its height $h$?

    $8$. Since $V=Bh$, then $h=\frac{V}{B}=\frac{96}{12}=8$.

29. What is the volume of a right rectangular prism with $l=5$, $w=3$, and $h=4$?

    $60$. Volume equals $lwh$: $(5)(3)(4)=60$.

30. State the formula for the volume of a right prism with base area $B$ and height $h$.

    $V=Bh$. Prism volume equals base area times height.

31. What is the area of a triangle with base $b=10$ and height $h=6$?

    $A=30$. Apply $A=\frac{1}{2}bh$: $\frac{1}{2} \times 10 \times 6 = 30$.

32. What is the area of a trapezoid with $b_1=6$, $b_2=10$, and $h=5$?

    $A=40$. Apply formula: $\frac{1}{2}(6+10) \times 5 = \frac{1}{2} \times 16 \times 5 = 40$.

33. Find the volume of a right triangular prism with base area $B=18$ and height $h=4$.

    $72$. Using $V=Bh$: $(18)(4)=72$.

34. Find the area of a triangle with $b=10$ and $h=6$.

    $30$. Using $A=\frac{1}{2}bh$: $\frac{1}{2}(10)(6)=30$.

35. What is the area formula for a parallelogram with base $b$ and height $h$?

    $A=bh$. Base times perpendicular height for any parallelogram.

36. What is the area of a triangle with $b=10$ and $h=6$?

    $30$. Using $A=\frac{1}{2}bh$: $\frac{1}{2}(10)(6)=30$.

37. What is the volume of a rectangular prism with $l=5$, $w=2$, and $h=3$?

    $V=30$. Apply $V=lwh$: $5 \times 2 \times 3 = 30$.

38. What is the area of a parallelogram with $b=12$ and $h=7$?

    $84$. Using $A=bh$: $(12)(7)=84$.

39. Find the area of a parallelogram with $b=9$ and $h=4$.

    $36$. Using $A=bh$: $(9)(4)=36$.

40. What is the perimeter formula for a rectangle with length $l$ and width $w$?

    $P=2l+2w$. Sum of all four sides: two lengths plus two widths.

41. Find the volume of a right rectangular prism with $l=6$, $w=2$, and $h=5$.

    $60$. Volume equals $lwh$: $(6)(2)(5)=60$.

42. State the formula for the lateral area of a right prism with base perimeter $P$ and height $h$.

    $L=Ph$. Lateral area equals base perimeter times prism height.

43. What is the surface area of a cube with side length $s=5$?

    $150$. Using $SA=6s^2$: $6(5^2)=6(25)=150$.

44. What is the surface area formula for a cube with side length $s$?

    $SA=6s^2$. Six square faces, each with area $s^2$.

45. State the formula for the surface area of a cube with side length $s$.

    $SA=6s^2$. A cube has 6 square faces, each with area $s^2$.

46. What is the circumference formula for a circle with radius $r$?

    $C=2\pi r$. Distance around circle is $2\pi$ times radius.

47. State the formula for the surface area of a right prism using lateral area $L$ and base area $B$.

    $SA=L+2B$. Prism surface area adds lateral area plus both bases.

48. Find the area of a trapezoid with $b_1=8$, $b_2=12$, and $h=5$.

    $50$. Using $A=\frac{1}{2}(b_1+b_2)h$: $\frac{1}{2}(8+12)(5)=50$.

49. Find the surface area of a right prism with base perimeter $P=20$, height $h=7$, and $B=24$.

    $188$. Using $SA=Ph+2B$: $(20)(7)+2(24)=140+48=188$.

50. What is the area formula for a circle with radius $r$?

    $A=\pi r^2$. Pi times radius squared gives circular area.

51. What is the surface area formula for a right prism using base area $B$ and base perimeter $P$?

    $SA=2B+Ph$. Two bases plus lateral area (perimeter times height).

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