Question

In the diagram, ABCD is an isosceles trapezoid. Its bases are AB and CD. BA is extended to E, and DE and EB are perpendicular. Side BC is a diameter of semicircle O, AB=4, AE= 3,DE=4, and DC=10.

Answer 1

a) the length of AD is _____________units
b)the area of the entire figure to the nearest integer is ____________square units.

Answer 2

since DEA makes 90degrees, AD is just the hypotenuse from the pythagorean theorem

Answer 3

hypotenuse is \[sqrt(a^2+b^2)\]

Answer 4

so sqrt(3^2+4^2)

Answer 5

yes, so \[\sqrt(25)\]

Answer 6

\[\sqrt{25}=5\]

Answer 7

a is right but b wrong

Answer 8

yes, as far as the full area of the whole composite, just add all adjacent figures
you have there a triangle, a trapezoid, and a circle/2[semicircle], so \[1/2(3)(4)\] for the triangle PLUS \[4/2(4/10)\] for the trapezoid PLUS \[2\pi*r^2\]
now keep in mind that the semicircle has a diameter of 4, the long line to the left, so half that is the radius, or "r"

Answer 9

hold, the long line on the semicircle isn't 4 :/, is a bit more, since is not a straight line is slanted

Answer 10

so how to solve it

Answer 11

if you were to extend B by 3more units, EB would become 10, just like DC, a 10x4 rectangle, so, let me draw it

Answer 12

from the graph, notice that the hypotenuse for THAT triangle, will be the same as the one on the other side, and thus that diameter will be \[\sqrt(25)\]

Answer 13

Hint ad is a hypotenuse of aright triangle the general strategy for computing the area of a combined figure is to divide the region up into individual components whose areas are easier to find, and then add up the areas.In this case, the region is a combination f a right triangle a trapezoid and a semicircle.

Answer 14

right

Answer 15

which is what you're already doing

Answer 16

so the diameter is 5 for the semicircle, the radius is half that and thus \[2pi*r^2\] added to the other 2 areas will be it

Answer 17

it was wrong answer b 44

Answer 18

....hmm, I put in (3*4*1/2)+(4/2*(4+10))+(pi*5^2) and got something else

Answer 19

rechecking

Answer 20

is not 44 here :|

Answer 21

it is 44