An oval track is made by enclosing semicircles on each end of a 52 m by 104 m rectangle. Find the area enclosed by the track. Use 3.14 for a.

7,540.64 m^2

Step-by-step explanation:

The area enclosed by the track may be computed as the sum of the area of the 2 semicircles and a rectangle.

The area of a semicircle is given as

A = 1/2 Pi r^2 where r is the radius of the semicircle. Since there are 2 semicircles, the area of the two will be

= Pi r^2

r = 52/2 = 26 m

Hence the area of the two semicircles

=3.14 * 26^2

= 2,122.64 m^2

The area of the rectangle is the product of its length and width

= 104 * 52

= 5408 m^2

Total area covered by the track

= 2,122.64 + 5,408

= 7,540.64 m^2

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.

17 1/3

step-by-step explanation: