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≈ 36.5 cm²

Step-by-step explanation:

Given the perimeters in ratio a : b , then

ratio of areas = a² : b²

Here ratio of perimeter = 20 : 28 = 5 : 7 , thus

ratio of areas = 5² : 7² = 25 : 49

let x be the area of larger , then using proportion

= ( cross- multiply )

25x = 911.4 ( divide both sides by 25 )

x ≈ 36.5 cm² ( to the nearest tenth )

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

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step-by-step explanation: