In a rectangular trapezoid ABCD, the angle is A = 90 degrees. The bases are 8cm and 11cm
In a rectangular trapezoid ABCD, the angle is A = 90 degrees. The bases are 8cm and 11cm, the lateral side is CD = 5cm. find the area of the trapezoid.
A trapezoid is a quadrilateral in which two sides are parallel and the other two are not parallel.
A rectangular trapezoid is called, in which one side is perpendicular to the bases.
The area of the trapezoid is calculated using the following formula:
S = (a + b) / 2 ∙ h, where:
S is the area of the trapezoid;
a – smaller base;
b – larger base;
h is the height of the trapezoid;
In order to find the area of a trapezoid, you need to calculate its height. For this, consider the triangle ΔСDН. This triangle is rectangular.
To calculate the length of the CH, we use the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the legs:
CD ^ 2 = CH ^ 2 + HD ^ 2;
CH ^ 2 = CD ^ 2 – HD ^ 2;
CH ^ 2 = 5 ^ 2 – 3 ^ 2 = 25 – 9 = 16;
CH = √16 = 4 cm;
S = (8 + 11) / 2 4 = 19/2 ∙ 4 = 38 cm2.
Answer: the area of the trapezoid is 38 cm2.