- 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 involving rectangles and triangles

In this lesson we solve problems involving rectangles and triangles. We are given rectangles. In these rectangles, triangles are drawn or cut off and the remaining area or area between rectangle and triangle is to found.

**a.** For example we have a rectangle and triangle as follows

We are required to find the area between the rectangle and the triangle

**Area of shaded region = Area of rectangle – Area of triangle**

**b.** For example we have a triangle cut off from a rectangle as follows

We are required to find the area of the remaining part of the rectangle which is shaded.

**Area of shaded region = Area of rectangle – Area of triangle**

Find the area of the shaded region in the following figure.

### Solution

**Step 1:**

Area of rectangle = l × w = 8 × 6 = 48 sq m; Area of triangle = $\frac{1}{2}$ b h = $\frac{1}{2}$ × 6 × 4 = 12 sq m

**Step 2:**

Area of shaded region = Area of rectangle – Area of triangle

= 48 – 12

= 36 square m

Find the area of the shaded region in the following figure.

### Solution

**Step 1:**

Area of rectangle = l × w = 8 × 5 = 40 sq ft; Area of triangle = $\frac{1}{2}$ b h = $\frac{1}{2}$ × 4 × 3 = 6 sq ft

**Step 2:**

Area of shaded region = Area of rectangle – Area of triangle

= 40 – 6

= 34 square ft