Find the area of a rectangular trapezoid, the bases of which are equal to 14 and 26

Find the area of a rectangular trapezoid, the bases of which are equal to 14 and 26, the large side makes an angle of 45 degrees with the base.

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

S = (a + b) / 2 h.

Since this trapezoid is rectangular, this means that the corners adjacent to its smaller side side are straight, and its height is equal to the length of the smaller side side:

∠С = ∠D = 90º;

ВН = СD.

The НD segment is equal to the length of the smaller base BC, since it is located between the perpendiculars of the trapezoid.

The length of the segment AH is equal to:

AН = AD – НD;

AH = 26 – 14 = 12 cm.

Consider the triangle ΔАВН. This triangle is rectangular. Since the value of the angle ∠А is equal to 45º, and the angle ∠Н is a straight line, the angle ∠В is equal to:

∠В = 180º – ∠А – ∠Н;

∠В = 180º – 45º – 90º = 45º.

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

tg B = AH / BH;

BH = AH / tg B;

tg 45º = 1;

BH = 12/1 = 12 cm.

Now let’s calculate the area of ​​the trapezoid:

S = (14 + 26) / 2 * 12 = 40/2 * 12 = 20 * 12 = 240 cm2.

Answer: the area of ​​the trapezoid is 240 cm2.