Area of Polygons & Composites - Pre Algebra

1. What is the formula for the area of a rhombus with diagonals $d_1$ and $d_2$?

   $A = \frac{d_1 d_2}{2}$. The diagonals split it into four congruent right triangles.

2. What is the formula for the area of a parallelogram?

   $A = bh$, where $h$ is the perpendicular height, not the slanted side.

3. What is the area of a rhombus with diagonals 18 cm and 24 cm?

   216 square centimeters, since $\frac{18 \cdot 24}{2} = 216$.

4. What is the area of a parallelogram with base 16 in and height 9 in?

   144 square inches, since $16 \times 9 = 144$.

5. What is the area of a triangle with base 10 cm and height 7 cm?

   35 square centimeters, since $\frac{1}{2}(10)(7) = 35$.

6. What is the formula for the area of a triangle?

   $A = \frac{1}{2}bh$, where $h$ is the height perpendicular to the base $b$.

7. What is the area of a trapezoid with bases 6 m and 10 m and height 4 m?

   32 square meters, since $\frac{1}{2}(6 + 10)(4) = 32$.

8. A 3 ft by 2 ft rectangle is cut out of a 10 ft by 8 ft rectangle. What area remains?

   74 square feet, since $80 - 6 = 74$.

9. What is the formula for the area of a trapezoid?

   $A = \frac{1}{2}(b_1 + b_2)h$, where $b_1$ and $b_2$ are the parallel bases.

10. What is the strategy for finding the area of a composite figure?

    Split it into simpler shapes, find each area, then add them (or subtract the areas of any cut-out parts).

11. Why does a parallelogram have the same area formula, $A = bh$, as a rectangle?

    A right triangle cut from one end can be moved to the other end, forming a rectangle with the same base and height.

12. A triangle with base 12 m and height 4 m sits on top of a 12 m by 5 m rectangle. What is the total area?

    84 square meters: the rectangle is 60 and the triangle is $\frac{1}{2}(12)(4) = 24$.

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