In a rectangular trapezoid, the bases are 12 cm and 30 cm, and the large side side is equal to 2√145 find the area of a quadrilateral whose vertices are the vertices of the sides of the trapezoid.
The area of the required figure is found as the sum of the areas of a square and a right-angled triangle.
In the square, to find the area, it is enough to find the height of the trapezoid. Find both legs in the triangle.
One of the legs of the triangle is the same height of the trapezoid. The second leg is the difference between the bases of the trapeziums:
30 – 12 = 18 cm – the first leg of the triangle.
We find the second leg of the triangle from the Pythagorean theorem:
x ^ 2 = 4 * 145 – 324 = 580 – 324 = 256 cm².
x = 16 cm.
S = S1 + S2;
S = 16 * 12 + 16 * 18 * 1/2 = 192 + 144 = 336 cm².
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