To find the area of a composite figure, we generally need to know the specific shapes that make up the composite figure and how they are arranged. However, based on the side lengths provided (3, 4, 9, and 10), we can't determine the exact configuration without further information.
If we assume these lengths represent the sides of a rectangle and the heights associated with them, we can use basic area formulas. Here are some possible interpretations:
- Rectangle: If the sides are lengths of a rectangle, we can calculate the area directly.
- Triangle or other shapes: If we assume they might be associated with triangles, circles, or other shapes, the approach would differ.
However, given those specific side lengths (3, 4, 9, 10) don't provide a clear configuration, but for the purpose of demonstration, let's compute using a rectangle and some triangles:
Example Calculation 1: Rectangle
Assuming pairs such that:
- length = 10 and width = 9
Area = length × width = 10 × 9 = 90 square units.
This is not one of your provided options.
Example Calculation 2: Triangles
If we use two triangles and rectangles or quadrilaterals:
For example, if one triangle has a base of 9 (half the rectangle) and height of 4: Area of Triangle = 1/2 × base × height = 1/2 × 9 × 4 = 18 square units.
If another triangle has a base of 3 and height of 10: Area of Triangle = 1/2 × 3 × 10 = 15 square units.
These total 33 square units which again isn't an option.
Valid Options
With valid options being 57.5, 67, 218, or 102.5 square units, and based only on the provided side lengths the areas individually do not sum up to any of those concise units unless combining various geometric configurations in a methodically improper structure.
Given all of these hypothetical configurations don't lead to any of the answer options, proper shape definitions and orientation are required.
Final Note
Please share more information or a diagram related to the composite shape you are trying to find the area for. With this information, we can provide an accurate area query.