- Perimeter and Area of Polygons
- Home
- Sides of polygons having the same perimeter
- Finding the missing length in a figure
- Perimeter of a piecewise rectangular figure
- Area of a rectangle involving fractions
- Distinguishing between the area and perimeter of a rectangle
- Areas of rectangles with the same perimeter
- Word problem involving the area of a square or a rectangle
- Finding the side length of a rectangle given its perimeter or area
- Area of a piecewise rectangular figure
- Area between two rectangles
- Finding the area of a right triangle on a grid
- Finding the area of a right triangle or its corresponding rectangle
- Area of a triangle
- Finding the area of a trapezoid on a grid by using triangles and rectangles
- Area involving rectangles and triangles
- Area of a parallelogram
- Area of a trapezoid
- Finding the perimeter or area of a rectangle in the coordinate plane

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# Area of a piecewise rectangular figure

In this lesson we find the area of given piecewise rectangular figures. The figures are broken down into two or more rectangles and their areas are found. The sum of the areas of these rectangles gives the area of the piecewise rectangular figure.

Consider the following piecewise rectangular figure. We have to find its area.

This figure can be considered as being made of two rectangles of dimensions 7 × 2 and 3 × 3 or 5 × 3 and 4 × 2

Finding the areas of the set of two rectangles gives the area of the piecewise rectangular figure.

Area = 7 × 2 + 3 × 3 14 + 9 = 23 square units

Area = 5 × 3 + 4 × 2 = 15 + 8 = 23 square units

Find the area of piecewise rectangular figure given below.

### Solution

**Step 1:**

Area of a rectangle = l × w; l = length; w = width

**Step 2:**

Area of 2 piecewise rectangles = 3 × 3 + 7 × 2 = 23 square units

Find the area of piecewise rectangular figure given below.

### Solution

**Step 1:**

Area of a rectangle = l × w; l = length; w = width

**Step 2:**

Area of 2 piecewise rectangles = 4 × 9 + 10 × 4 = 76 square units