How to Find the Surface Area of Composite Figures

Area of Composite Shapes

The area of composite shapes is the area that is covered by any composite shape. The composite shape is a shape in which few polygons are put together to form a required shape. These shapes or figures can be made up of a combination of triangles, squares, and quadrilaterals, etc. Divide a composite shape into basic shapes like square, triangle, rectangle, hexagon, etc. to determine the area of composite shapes.

Basically, a composite shape is made up of basic shapes put together. It is also called a "composite" or "complex" shape. The area of the composite shape is explained in this mini-lesson along with solved examples and practice questions.

1.	What is the Area of Composite Shapes?
2.	How to Find Area of Composite Shapes?
3.	FAQs on Area of Composite Shapes

What is the Area of Composite Shapes?

The area of the composite shapes is the area of combined shapes of one or more simple polygons and circles. To calculate the area of the composite shapes we can add the areas of all the basic shapes together. In order to find the area of composite shapes, simply find the area of each shape and add them together. The following figure will give an idea about finding the area of a composite shape. The unit of the area of composite shapes is expressed in terms of m², cm², in² or ft², etc.

How to Find Area of Composite Shapes?

The area of composite shapes is a combination of basic shapes. By the following steps mentioned below, we can calculate the area of the composite shapes.

• Step 1: Break the compound shape into basic shapes.
• Step 2: Find the area of each and every basic shape.
• Step 3: Add all the areas of basic shapes together.
• Step 4: Represent the answer in square units.

In order to decompose any composite shape, we must know to calculate the area of some basic shapes like squares, triangles, rectangles, and so on. Check the table below containing the area of the basic shapes.

Name of Basic Shape	Area of Basic Shape
Triangle	Area of triangle = (1/2) × base × height. It is also possible to find the area of a triangle if the length of its sides is known by using Heron's formula. As per the formula, Area = \(\sqrt{s(s-a)(s-b)(s-c)}\), where s = Perimeter/2 = (a + b + c)/2, a, b, and c are the length of its sides.
Square	Area of square = (length)2
Rectangle	Area of rectangle = length × breadth
Parallelogram	Area of parallelogram = base × height
Trapezium	Area of trapezium = (1/2) × (sum of lengths of parallel sides) × height
Rhombus	Area of rhombus = (1/2) × (product of diagonals)

Example: Find the area of the composite shape which is formed by joining a square and a triangle. The length of the side of the square is 5 units. The base and height of the triangle are 6 units and 7 units respectively.

Solution: Given the length of the side of the square = 5 units, the base of the triangle = 6 units, and the height of the triangle = 7 units

Area of composite shape = Area of square + Area of triangle
⇒ A = (5)² + [(1/2) × 6 × 7]
⇒ A = 25 + 21 = 46 square units

The area of the composite shape is 46 square units.

Solved Examples on Area of Composite Shapes

1. Example 1: Calculate the area of this composite shape which is given in the figure below.
   

   Solution: The length and breadth of rectangle ABCD are 2 in and 7 in.
   The length of the side of the square DEFG is 3 in.

   Using the formula for the area of the composite shape,

   Area of composite shape = Area of rectangle + area of the square.
   ⇒ Area of composite shape = Length × Breadth + side²
   ⇒ Area of composite shape = BC × AB + DE²
   ⇒ Area of composite shape = 2 × 7 + 3²
   ⇒ Area of composite shape = 14+9 = 23 square inches.

   Therefore, the area of the given composite shape is 23 square inches.

2. Example 2: A composite shape has an area of 500 units square. The shape is composed of a circle and a triangle and the area of the triangle is 350 units square. What is the area of the circle?

   Solution: Given the area of a composite shape = 500 units square and area of triangle = 350 units square

   Using the formula for the area of the composite shape, Area of composite shape = area of triangle + area of the circle.
   ⇒ 500 = 350 + area of circle
   ⇒ Area of circle = 500 - 350
   ⇒ Area of the circle = 150 units square.

   Therefore, the area of the circle is 150 units square.

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Practice Questions on Area of Composite Shapes

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FAQs on Area of Composite Shapes

What is the Area of Composite Shapes?

The area of composite shapes is defined as the area covered by any composite shape. A composite shape is made up of basic shapes put together. Thus, the area of the composite shape is found by individually adding all the basic shapes.

What is the Area of Composite Shapes Formula?

There is no fixed formula to determine the area of composite shapes. The area of composite shapes can be calculated by dividing the composite shape into basic shapes like square, triangle, circle, rectangle, polygon, etc. and add their areas.

What is the Unit of the Area of Composite Shapes?

The area of composite shapes can be found out by adding all the areas of figures together. The unit of the area of composite shapes is expressed in square units like m², cm², in² or ft², etc.

How to Find the Area of Composite Shapes?

The steps for finding the area of composite shapes are:

• Step 1: Divide the compound shape into basic shapes.
• Step 2: Find the area of each basic shape separately.
• Step 3: Add all the areas of basic shapes together.
• Step 4: Now, write the answer in square units.

How to Find the Area of Composite Shapes If the Areas of All the Basic Shapes In It are Known?

The area of composite shapes if the areas of all the basic shapes in it are known is found by using the following steps:

• Step 1: Identify the individual area of all basic shapes.
• Step 2: Add the areas of all basic shapes together.
• Step 3: Now, write the answer in square units.

What Happens to the Area of Composite Shapes If the Dimensions of all the Basic Shapes are Increased?

If the dimensions of all the basic shapes are increased, the area of composite shapes also increases. The area of composite shape changes as it depends on the individual area of basic shape which gets changed when the dimensions are increased.

How to Find the Surface Area of Composite Figures

Source: https://www.cuemath.com/measurement/area-of-composite-shapes/

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