Find the area of a rectangular trapezoid, the large base of which is 24cm, the smaller side is 10cm

Find the area of a rectangular trapezoid, the large base of which is 24cm, the smaller side is 10cm, and the obtuse angle is 135 degrees.

Rectangular is a trapezoid in which the corners adjacent to one side are straight:

∠С = ∠D = 90º.

In order to calculate the area of ​​a trapezoid, you need to multiply the half-sum of its bases by the height:

S = (a + b) / 2 h.

The height of this trapezoid is equal to the length of its smaller lateral side:

ВН = СD = 10 cm.

Find a smaller base. Since the segments BC and HD are equal, then:

BC = НD = AD – AН.

It is necessary to find the length of the segment AH. To do this, consider the triangle ΔАВН.

Angle ∠АВН = ∠АВС – ∠НВС;

∠AВН = 135º – 90º = 45º.

To calculate AH, we use the tangent of the angle ∠B:

tg B = AH / BH;

tg 45º = 1;

AH = BH · tg B;

AH = 10 1 = 10 cm.

BC = НD = 24 – 10 = 14 cm.

Now we can find the area of ​​the trapezoid:

S = (14 + 24) / 2 · 10 = 38/2 · 10 = 19 · 10 = 190 cm2.

Answer: the area of ​​the trapezoid is 190 cm2.