Abcd is a trapezoid with ad = 5 ft, dc = 7 ft, and ab = 15 ft. find the area of the trapezoid. 30 ft2 33 ft2 44 ft2 55 ft2

33 ft².

Step-by-step explanation:

1. As you can see in the figure attached, the trapezoid is formed by a rectangle and two equal right triangles. The base of each triangle is 4 feet and you know the lenght of the hypotenuse AD, therefore, you can calculate the height by applying the Pythagorean Theorem:

2. Now, you can calculate the area with the following formula:

Where B is the longer base, b is the shorter base and h is the height.

Then:

D.

Step-by-step explanation:

The area of the trap-ezoid ABCD is given by the formula,

See diagram in the attachment.

We substitute the given values to obtain;

This simplifies to

This will give us;

Therefore the correct answer is option D.

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

so, converting firstly the mixed fractions to improper fractions and then "adding".