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A.)555 in.^2

Step-by-step explanation:

When solving these types of things, I usually like to cut it up into smaller, easier to manage shapes.

You can cut that trapezoid into two triangles and one rectangle.

Since both triangles are the same size, you don't need to divide the base and height by two, so you'll get the area of both triangles combined (which saves some work).

We know the length of the rectangle and bases of the triangle combined is 44 inches, and that the length of just the rectangle is 30 inches, so we can just subtract 30 from 44 and divide it by two for the base of a triangle.

                                                     44 - 30 = 14

                                                     14/2 = 7

Now that we filled in the information not listed, we can finally solve:

The base of one triangle is 7 inches, and the height is 15 inches.

Now, we just multiple and divide it by 2 for one triangle (it would be 52.5 inches).

But, we don't need to divide it by two because both triangles are the same size, so we can just get the sum of the area of both triangles combined by skipping that step (because triangles are half a square and two of those triangles make a full square).

7 x 15 = 105

The area of both triangles combined: 105 in.^2

Next, we need to solve the area of the rectangle. This is easy considering all you have to do is multiply 15 by 30 (length times width).

15 x 30 = 450

The area of the rectangle: 450 in.^2

Now, the final step. Addition. All you need to do is add up all the sums, and you're done.

450 + 105 = 555

The area of entire figure: 555 in.^2

NOTE: the symbol '^' represents exponents, so when you see 555 in.^2, it means inches squared (or to the power of 2)

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.