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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Area of a trapezoid
Area of a trapezoid
The trapezoid has one pair of parallel opposite sides called the bases b1 and b2. The height h of the trapezoid is perpendicular distance between these bases.
Formula to find area of a trapezoid
Area of a trapezoid = $left [ frac{left ( b_1 + b_2 ight )}{2} ight ] imes h$
where h is the height and b1 and b2 are the bases.
We multiply the average of the bases of the trapezoid with the height of the trapezoid to get its area.
Find the area of the following trapezoid.
Solution
Step 1:
Area of Trapezoid = $frac{1}{2}$ × h × (b1 + b2); b1, b2 = bases = 3, 4.5; h = height = 5.
Step 2:
Area of trapezoid = $frac{1}{2}$ × 5 × (3 + 4.5) = 18.75 square in
Find the area of the following trapezoid.
Solution
Step 1:
Area of Trapezoid = $frac{1}{2}$ × h × (b1 + b2); b1, b2 = bases = 5, 8; h = height = 4.4.
Step 2:
Area of trapezoid = $frac{1}{2}$ × 4.4 × (5 + 8) = 28.6 square in