AREA OF GEOMETRIC SHAPES – COMPOSITE

Concept: Area is a measure of the surface of a flat figure. Area is measured in square units. Area tells how many square units it takes to cover the space inside the figure. Listed below are the formulas for finding the area of geometric shapes. A figure may be made up of several shapes. To find the area of a combined figure, find the area of each of the parts and add the results.

Chart of Formulas for Finding the Area of Geometric Shapes
Square | A = s2 |
Rectangle | A = lw |
Triangle | A = bh |
Circle | A = r2 |
Parallelogram | A = bh |
Trapezoid | A = (b1 + b2)h |

Steps for Finding the Area of Geometric Shapes

Step 1 | Divide the figure into simple shapes.
Step 2 | Choose the proper formula for the first shape in the problem.
Step 3 | Substitute the values.
Step 4 | Solve.
Step 5 | Repeat Steps 2, 3, and 4.
Step 6 | Combine areas.
Step 7 | Write the final answer.

Example Solve for s, given total area = 13.07, a = 3, and pi =3.14

| Begin by finding the area of the circle. Next, subtract the area of the circle from the total area. The difference is the area of the triangle. Solve for height in the triangle. Add the height of the triangle and the diameter of the circle to solve for S. |
Step 1 | Divide the figure into simple shapes. | A = bh A =r2
Step 2 | Choose the proper formula for the first shape in the problem. | A =r2
Step 3 | Substitute the values. | A = 3.14 x 1.52
Step 4 | Solve. | A = 3.14 x 1.52 A = 3.14 x 2.25 A = 7.065 A = 7.07
| Next, subtract the area of the circle from the total area. | 13.07 – 7.07 = 6
| The difference is the area of the triangle. | A = 6
| Solve for height in the triangle. |
Step 5 (Step 2) | Repeat Steps 2, 3, and 4. Choose the proper formula for the second shape in the problem. | A = bh
Step 5 (Step 3) | Substitute the values. | 6 = x 3 x h
Step 5 (Step 4) | Solve. | 6 = x 3 x h 6 = 1.5 x h 6 = 1.5 x h 1.5 1.5 4 = h
Step 6 | Combine areas. Add the height of the triangle and the diameter of the circle to solve for S. | 4 + 3 = 7
Step 4 | Write the final answer. | S = 7