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natali 33 [55]
3 years ago
9

GEOMETRY | can some please help me? i'm really confused (20 POINTS + BRAINLIEST)

Mathematics
2 answers:
iogann1982 [59]3 years ago
7 0

(The Answer) : D not A, B, and C

Mademuasel [1]3 years ago
5 0

This is the last answer because if you reflect it 4 times over the x and y axis you will get back to the same spot


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In parallelogram ABCD, AB = 16 cm, DA = 3<img src="https://tex.z-dn.net/?f=%5Csqrt%7B2%7D" id="TexFormula1" title="\sqrt{2}" alt
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Answer:

length of segment YZ is 8 cm

Step-by-step explanation:

given data

AB = 16 cm

DA = 3\sqrt{2} cm

AB and DA form interior angle  =  45-degre

WX ≠ YZ

WX = 16 cm

to find out

length of segment YZ

solution

area of △ABD is  the same as the area of △BCD

and

area of △ABD is express as

area of △ABD = AB × AD × sin(45) ÷ 2    ............1

put here value

area of △ABD = 16 × 3√2 × sin(45) ÷ 2

area of △ABD = 24

and

area of the parallelogram is

area of the parallelogram = 24 × 2

area of the parallelogram = 48

so

now we will consider here YZ = x

and Since ZY XW is isosceles trapezoid

so here we can say that

WM = ZM = (16 - x)  ÷ 2   .......................2

so area of  trapezoid will be

area of  trapezoid = \frac{ZY + WX }{2}  \times ZM         .......................3

area of  trapezoid = \frac{x+16}{2} \times \frac{16 - x}{2}    

48 = \frac{x+16}{2} \times \frac{16 - x}{2}  

solve it we get

x = 8

so length of segment YZ is 8 cm

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