Germany · Klasse 7 · Practice Sheet 25

1. 1.

   A right-angled triangle has legs of 19 cm and 11 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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2. 2.

   A triangle has a base of 5 cm and a height of 16 cm. Find its area.

   Formula:Area of a Triangle

   $A = \tfrac{1}{2} b h$

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3. 3.

   Find the area of a square with side length 17 cm.

   Formula:Area of a Square

   $A = s^2$

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4. 4.

   A right-angled triangle has legs of 8 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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5. 5.

   Find the perimeter of a rectangle measuring 35 m by 7 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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6. 6.

   A triangle has a base of 33 cm and a height of 30 cm. Find its area.

   Formula:Area of a Triangle

   $A = \tfrac{1}{2} b h$

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7. 7.

   A circle has a radius of 25 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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8. 8.

   Solve for x: 5x + 2 = 57.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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9. 9.

   A value changes from 104 to 102. Find the percentage change (to 2 d.p.).

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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10. 10.

    Find the circumference of a circle whose radius is 15 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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11. 11.

    Find 1/2 of 24.

    Formula:Fraction of a Quantity

    $\text{result} = \dfrac{a}{b} \times N$

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12. 12.

    A circle has a radius of 11 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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13. 13.

    Find the perimeter of a rectangle measuring 30 m by 9 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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14. 14.

    A value changes from 73 to 238. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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15. 15.

    A rectangle is 10 cm long and 5 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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16. 16.

    A triangle has a base of 34 cm and a height of 16 cm. Find its area.

    Formula:Area of a Triangle

    $A = \tfrac{1}{2} b h$

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17. 17.

    A circle has a radius of 17 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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18. 18.

    A value changes from 39 to 63. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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19. 19.

    A circle has a radius of 3 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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20. 20.

    €1,100 is invested at 6% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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