- 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
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