Calculate the Area of a Composite Figure

Published on September 3, 2026

Geometry

Find the area of a complex geometric figure by dividing it into simpler rectangles and triangles, and summing their individual areas to get 117 square meters.

Question

Answer

To find the area of the figure, we can decompose it into simpler geometric shapes: a triangle and a rectangle.
Step 1: Identify the dimensions of the base rectangle.
The bottom-most part of the figure is a rectangle. Looking at the right side, the total height is . The total width at the bottom is (or by looking at the top, ). However, it is easier to split the figure vertically.
Let’s split the figure into a right-side rectangle and a left-side composite shape.
  • The rightmost rectangle has a width of and a height of .
Step 2: Calculate the area of the remaining left section.
The remaining section is a trapezoid-like shape. We can split this into a rectangle and a triangle.
  • The bottom rectangle of this section has a width of and a height of .
  • The top part is a triangle. The base of the triangle is the width of the section above the height. The total width of the figure is .
    The triangle’s base is .
    The height of the triangle is .
Step 3: Sum the areas.
Final Answer: square meters