In trapezoid, two triangles are formed by the bases and the intersecting diagonal segments. the areas of these triangles are s1 and s2. find area of the trapezoid in terms of s1 and s2.

Step-by-step explanation:

Consider trapezoid ABCD. Let triangle BEC be of area and triangle AED be of area

Triangles BEC and AED are similar with the coefficient of similarity

Consider triangles ABC and ACD. The area of these triangles are

Note that

where is the height of the triangle BEC, is the height of the triangle AED and

Thus,

and

or

Then

Thus, the area of trapezoid ABCD is

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.