The diagonals of the trapezoid are mutually perpendicular and equal to 4 and 10 cm. Find the area of the trapezoid.
| February 12, 2021 | education
From the condition it is known that the diagonals of the trapezoid are mutually perpendicular and it is also known that their lengths are 4 and 10 cm, respectively. And we need to find the area of the trapezoid.
To find the area of a trapezoid, we will apply the formula for finding the area in terms of the lengths of the diagonals and the angle between them.
S = 1/2 * d1 * d2 * sin a.
Let’s find the sine of the angle a before substituting the values into the formula.
sin 90 = 1.
It remains only to substitute the values into the formula and perform calculations:
S = 1/2 * 4 * 10 * 1 = 40/2 = 20 cm ^ 2.
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