find the area of the trapezoid by decomposing it into other shapes.
a) 25 cm?
b) 27 cm?
c) 30 cm?
d) 35 cm?

C

Step-by-step explanation:

You can decompose it into two triangles and one rectangle. The rectangle has a length of 4 and the width is 5. The area of the rectangle is 20.

The right triangle has a height of 5 and a base of 1. You multiply it to get 5 then divide by 2. The right triangle has an area of 2.5.

The left triangle has a height of 5 and a base of 3. (7cm - 4 cm) Multiply to get 15 and divide by 2. The left triangle has an area of 7.5.

Add all three up.

20 + 2.5 +7.5

30

the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

: )

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)