# Basic Geometry – How to find the Area of Complex Shapes

- Posted by Brian Stocker
- Date October 9, 2017
- Comments 0 comment

### How to Find the Area of Complex Shapes

Complex figures can be divided into several smaller shapes where the perimeter or area formula is known, then added.

### Example – Composite 2-D shapes

To determine the area of any composite figure, simply ** ADD** the areas of each component basic figure. Be sure to write your final answer with square units.

**Determine the area of the given shape. **

The original shape can be redrawn as a rectangle and a triangle. Rectangles have opposite sides that are congruent (exactly the same).

Area _{Composite} = Area _{Triangle} + Area _{Rectangle}

Area _{Triangle} = (1/2)(Base)(Height) = (1/2)(3m)(1.5m) = 2.25 m^{2}

Area _{Rectangle }= (Base)(Height) = (3m)(1.5m) = 4.5 m^{2}

Area _{Composite} = (2.25m^{2}) + (4.5m^{2}) = 6.75 m^{2}

### How to find the area of a complex figure

To determine the surface area of any composite solid, simply **add** the surface areas of each component basic solid. You must also subtract the area of any internal face. Be sure to write your final answer with square units.

**Ex. Determine the surface area of the given shape. Leave the final answer in terms of pi.**

The original shape can be redrawn as a cylinder and a cone. We will have to subtract the area of the circle where the figures meet from each surface area equation because they are “inside” the solid.

SurfaceArea _{Composite} = S.Area _{Cone} + S.Area _{Cylinder}

S.Area _{Cone} = (Base Area)+(1/2)(Perimeter)(Height) = (1/2)(dπ)(h) = (1/2)(6π)(2) = 6π ft^{2}

S.Area _{Cylinder }= 2(Base Area)+(Perimeter)(Height) = (πr^{2})+(dπ)(h) = (π3^{2})+(6π)(5) = 39π ft^{2}

S.Area _{Composite} = (6π ft^{2}) + (39π ft^{2}) = 45π ft^{2}

### Most Popular Geometry Questions

**Common geometry questions on on standardized tests :**

- Solve for the missing angle or side
- Finding the area or perimeter of different shapes (e.g. triangles, rectangles, circles)
- Problems using the Pythagorean Theorem
- Calculate properties of geometric shapes such as angles, right angles or parallel sides
- Calculating volume or surface area of complex shapes for example spheres, cylinders or cones
- Solve geometric transformations such as rotation, translation or reflections

### Most Common Geometry Mistakes on a Test

- Not clearly labeling or identifying the given and unknown information in a problem
- Not understanding the properties and definitions of basic geometric figures (e.g. line, angle, triangle, etc.)
- Incorrectly using basic formulas (e.g. area of a triangle, Pythagorean theorem)
- Incorrectly interpreting geometric diagrams
- Not understanding the relationship between parallel lines and transversals
- Not understanding the relationship between angles and their degree measures
- Not understanding the relationship between perimeter and area

**Written by**, Brian Stocker MA., Complete Test Preparation Inc.

**Date Published:**Monday, October 9th, 2017

**Date Modified:**Monday, June 19th, 2023

Got a Question? Email me anytime - Brian@test-preparation.ca

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