The area of a trapezoid is 18 square meters. One base is 3 meters long and the other is 6 meters long. Find the height of the trapezoid. Step 2 of 3 : Without substitution, solve the formula chosen in the previous step for the unknown variable in terms of the known variable(s).

height = 4 meters

h = 2A / ( a +  b )

Step-by-step explanation:

Let A represent the area of the trapezoid, h, the height a, the length of one base and b, the length of the other base

Area of a trapezoid, A = ( a + b)* h / 2

Now let's slot in the given values

A= 18 sq meters

a = 3 meters

b = 6 meters

we have;

18 = ( 3 + 6 ) * h /2

18 = 9 * h /2

Cross multiply

18*2 = 9h

36 = 9h

divide both sides by the coefficient of h (9)

4 = h

therefore, h = 4 meters

To solve for h without substituting

From A = ( a + b )* h /2

cross multiply

2*A = ( a + b )* h

divide both sides by ( a + b )

2A / ( a + b ) = h

therefore,

h = 2A / ( a +  b )

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it