Hi, i need to know the work and answer to this. thanks!

Mathematics

1 answer:

Nesterboy [21]3 years ago

6 0

Answer:

432 in^2

Step-by-step explanation:

in similar quadrilaterals, the first point of one quad. corresponds to the first point of the other quad, so in this case UA corresponds with CH.

since CH is 3/4 the length of UA, we can also assume that the other sides in ZUCH are 3/4 the length of their corresponding sides in SQUA.

even though we don't know what quadrilateral SQUA and ZUCH are, we know the area of SQUA is 9/16 times less than ZUCH.

want some proof?

lets say SQUA and ZUCH are rectangle/square

ZUCH: 4X4 = 16

SQUA: 3X3 = 9

now lets say they are trapezoids. We will set ZUCH 2nd base to 8 and height to 16, therefore SQUA bases will be 3 and 6, and the height will be 12 (multiply ZUCH lengths by 3/4)

ZUCH = (b1+b2)(h)/2 = (4+8)(16)/2 = 96

SQUA = (b1+b2)(h)/2 = (3+6)(12)/2 = 54

simplify 96/54 = 16/9

now we can multiply 243 by our factor 16/9 to find the area of SQUA.

243 * 16/9 = 432 in^2

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