Geometry 2D - GED Math

1. A right triangle has legs of $6$ and $8$. What is the length of the hypotenuse?

   $10$. $6^2 + 8^2 = 36 + 64 = 100$, and $\sqrt{100} = 10$.

2. When can you use the Pythagorean theorem, and which side is $c$?

   Only in a right triangle: $a^2 + b^2 = c^2$, where $c$ is the hypotenuse, the side opposite the right angle.

3. What is the area of a circle with a diameter of $10$ cm?

   $25\pi$ square cm. The radius is half the diameter, $5$, and $A = \pi r^2 = 25\pi$.

4. In the triangle area formula $A = \frac{1}{2}bh$, what is $h$?

   The height: the perpendicular distance from the base to the opposite vertex, not the length of a slanted side.

5. What is the perimeter of a rectangle $9$ ft long and $6$ ft wide?

   $30$ ft. $P = 2l + 2w = 18 + 12$.

6. How do you find the area of a composite figure?

   Split it into simple shapes, find each area, and add them (subtract the area of any cut-out part).

7. What kind of units measure area, and what kind measure perimeter?

   Area uses square units (such as square feet); perimeter is a length, so it uses linear units (such as feet).

8. In the trapezoid area formula $A = \frac{1}{2}h(b_1 + b_2)$, what are $b_1$ and $b_2$?

   The lengths of the two parallel sides (bases). $h$ is the perpendicular distance between them.

9. A square has an area of $49$ square inches. What is its perimeter?

   $28$ inches. Each side is $\sqrt{49} = 7$, and $4 \times 7 = 28$.

10. What is the formula for the circumference of a circle?

    $C = 2\pi r$, or equivalently $C = \pi d$, where $r$ is the radius and $d$ the diameter.

11. If every side length of a figure is doubled, by what factor does its area change?

    It is multiplied by $4$. Area scales by the square of the scale factor: $2^2 = 4$.

12. What is the area of a parallelogram with base $12$ m and height $5$ m?

    $60$ square m. $A = bh = 12 \times 5$.

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