You probably learned how to calculate the area of known figures earlier in this course--or in another course. You may also remember hearing something about volume. When Ted flips through his old geometry notebook in order to refresh his memory, he finds some useful formulas and steps. See if you remember these too: Answer the question on each tab in your own mind before clicking the button to check your answer.
Rectangles and Squares
Triangles
Circles
| How do you calculate the area of rectangles and squares? | You multiply the length of the shape by its height. |
| What is the formula for finding the area of rectangles or squares? | \({ A = l \cdot w }\) |
| How do you calculate the area of a triangle? | You multiply one-half times the base of the triangle by the height. The height is the distance between the "top" point of the triangle and the base. It is not necessarily the length of a particular side. |
| What is the formula for finding area of a triangle? | \({ A = \frac{1}{2}(b \cdot h) }\) |
| How is the sine ratio used to calculate the area of a triangle with an unknown height? | Draw a line from a vertex perpendicular to its opposite side representing the height of the triangle. Now, choose two side lengths and their included angle. The height can now be written as a sine ratio. This is because it is equal to the hypotenuse multiplied by the sine of the included angle. Once the height is written as a sine ratio, multiply it to the other included side and \({ \frac{1}{2} }\) to solve for the area. |
| What is the formula for finding the area of a triangle with unknown height using sine? | \({ A = \frac{1}{2}a \cdot b \cdot \text{sin } 0 }\), where \({ a }\) and \({ b }\) are two side lengths and \({ 0 }\) is their included angle. |
| How do you calculate the area of a circle? | You square the radius of the circle and multiply that value by \({ \pi }\). |
| What is the formula for finding area of a circle? | \({ A = \pi \cdot r^{2} }\) |
