Question

to calculate the area of a compound shape, you should:
a. multiply its perimeter by the apothem
b. estimate the area without calculation
c. divide it into simpler shapes and sum their areas
d. use the formula for a complex

Explanation:

A compound shape is made up of simpler geometric shapes. To find its area, we break it into these simpler shapes (like rectangles, triangles, etc.). Then, we calculate the area of each simple shape using their respective area formulas (e.g., \(A = lw\) for rectangles, \(A=\frac{1}{2}bh\) for triangles). Finally, we sum up these individual areas.

• Option a: Multiplying perimeter by apothem is for regular polygons (not compound shapes in general).
• Option b: Estimating without calculation is not a valid method for an accurate area of a compound - shape problem (usually requires calculation).
• Option d: There is no single "formula for a complex" (compound) shape in the way described; we rely on decomposition.

Answer:

C. Divide it into simpler shapes and sum their areas