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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
Let’s split the figure into a right-side rectangle and a left-side composite shape.
The bottom-most part of the figure is a rectangle. Looking at the right side, the total height is
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 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: