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3. In the diagram, PRST and PQWV are rectangles. Q, V
and U are midpoints of PR, PU and PT respectively.
Find the area of the shaded region.​

3 In the diagram PRST and PQWV are rectangles Q Vand U are midpoints of PR PU and PT respectivelyFind the area of the shaded region class=

Respuesta :

Answer: 122.5 square cm

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Work Shown:

A = area of trapezoid RSTU

A = height*(base1+base2)/2

A = ST*(UT+RS)/2

A = 14*(5+10)/2

A = 105 square cm

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B = area of rectangle PQWV

B = length*width

B = WV*PV

B = 7*2.5

B = 17.5 square cm

If you're curious how I got PV = 2.5, you basically cut PT = 10 in half twice. So you go from 10 to 5, then from 5 to 2.5; which works because we have a bunch of midpoints.

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C = total shaded area

C = A + B

C = 105 + 17.5

C = 122.5