6 ways to find the area of ​​a trapezoid

1. How to find the area of ​​a trapezoid through the bases and height

Calculate the sum of the bases of the trapezoid.

Multiply the result by the height and divide by two.

• S is the required area of ​​the trapezoid.
• a and b - the bases of the trapezoid (its parallel sides).
• h is the height of the trapezoid.

2. How to calculate the area of ​​a trapezoid in terms of height and midline

Just multiply the height of the trapezoid by the centerline.

• S is the required area of ​​the trapezoid.
• m is the middle line of the trapezoid (the segment connecting the midpoints of the sides).
• h is the height of the trapezoid.

3. How to find the area of ​​a trapezoid through the diagonals and the angle between them

Multiply one diagonal by the other and then by the sine of any angle between them.

Divide the result by two.

• S is the required area of ​​the trapezoid.
• x and y are the diagonals of the trapezoid.
• α is any angle between the diagonals.

4. How to find the area of ​​a trapezoid across four sides

Subtract the smaller one from the larger base.

Find the square of the resulting number.

Add the square of one side to the result and subtract the square of the other.

Divide this number by twice the base difference.

Find the square of the result and subtract it from the square of the side.

Find the root of the resulting number.

Multiply the result by half the sum of the bases.

• S is the required area of ​​the trapezoid.
• a, b - bases of the trapezoid.
• c, d - sides.

5. How to calculate the area of ​​an isosceles trapezoid across four sides

Subtract the smaller one from the larger base of the trapezoid and divide the result by two.

Find the square of the resulting number and subtract it from the square of the side.

Find the root of the result.

Multiply the resulting number by the sum of the bases and divide by two.

• S is the required area of ​​the trapezoid.
• a, b - bases of the trapezoid.
• c, d - lateral sides (recall that in an isosceles trapezoid they are equal).

6. How to find the area of ​​an isosceles trapezoid through the in-circle radius and angle

Find the square of the radius and multiply it by four.

Divide the result by the sine of the known angle.

• r is the radius of the inscribed circle.
• α - any angle of the trapezoid.