Perimeter and Area of Polygons
Selected Reading
- Finding the perimeter or area of a rectangle in the coordinate plane
- Area of a trapezoid
- Area of a parallelogram
- Area involving rectangles and triangles
- Finding the area of a trapezoid on a grid by using triangles and rectangles
- Area of a triangle
- Finding the area of a right triangle or its corresponding rectangle
- Finding the area of a right triangle on a grid
- Area between two rectangles
- Area of a piecewise rectangular figure
- Finding the side length of a rectangle given its perimeter or area
- Word problem involving the area of a square or a rectangle
- Areas of rectangles with the same perimeter
- Distinguishing between the area and perimeter of a rectangle
- Area of a rectangle involving fractions
- Perimeter of a piecewise rectangular figure
- Finding the missing length in a figure
- Sides of polygons having the same perimeter
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Selected Reading
- Who is Who
- Computer Glossary
- HR Interview Questions
- Effective Resume Writing
- Questions and Answers
- UPSC IAS Exams Notes
Finding the area of a trapezoid on a grid by using triangles and rectangles
Finding the area of a trapezoid on a grid by using triangles and rectangles
In this lesson we find areas of trapezoids on grids by using triangles and rectangles. The trapezoids are decomposed into triangles and rectangles and their areas found. The sum of these areas gives the area of the trapezoid on the grid.
We know the area of a triangle = $frac{1}{2}$ b × h and
area of a rectangle = l × w
Find the area of the following trapezoid by using triangles and rectangles.
Solution
Step 1:
Area of Right Triangle = $frac{1}{2}$ × b × h; b = base; h = height.
Area of 2 right triangles = 2 × $frac{1}{2}$ × b × h = 1.5 × 4 = 6 square in.
Step 2:
Area of Rectangle = l × w = 4 × 3 = 12 square in
Step 3:
Area of trapezoid = Area of triangles + Area of rectangle
= 6 + 12
= 18 square in
Find the area of the following trapezoid by using triangles and rectangles.
Solution
Step 1:
Area of Right Triangle = $frac{1}{2}$ × b × h; b = base; h = height.
Area of 2 right triangles = 2 × $frac{1}{2}$ × b × h = 1 × 3 = 3 square in.
Step 2:
Area of Rectangle = l × w = 6 × 3 = 18 square in
Step 3:
Area of trapezoid = Area of triangles + Area of rectangle
= 3 + 18
= 21 square in