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ZanzabumX [31]
2 years ago
14

Please help me with the problem​

Mathematics
2 answers:
Ivan2 years ago
5 0

Exact Answers:

  • Area = 150.5*sqrt(3)
  • Perimeter = 57+7*sqrt(3)

Approximate Answers:

  • Area = 260.673646539
  • Perimeter = 69.12435565

======================================

Explanation:

Your diagram is 100% correct. Nice work.

To get the area of the trapezoid, we could use the area of a trapezoid formula below:

A = h*(b1+b2)/2

In this case, we have,

  • h = 7*sqrt(3) = height
  • b1 = 18 = base1
  • b2 = 25 = base2

the bases are parallel to each other. The height is always perpendicular to the base. We won't use the "14" at all.

So,

A = h*(b1+b2)/2

A = 7*sqrt(3)*(18+25)/2

A = 7*sqrt(3)*21.5

A = (7*21.5)*sqrt(3)

A = 150.5*sqrt(3)

This is the exact area.

The approximate area is roughly

150.5*sqrt(3) = 260.673646539

The units for the area are in square km, or km^2. Though your teacher said for you not to include the units.

Another way to get the area of the trapezoid is to break the diagram into a rectangle and triangle as you have done so, and then find the area of each sub-piece. Adding the two smaller areas should lead to the result shown above.

-----------------------------------

To get the perimeter, we add up all of the exterior sides. We do not include the right-most vertical line that is 7*sqrt(3) km long because it is inside the figure. The horizontal segment that is 7 km long is part of the "25 km" segment, so we'll ignore that 7.

Adding the four exterior sides leads to:

7*sqrt(3)+18+14+25 = 57+7*sqrt(3)

This value is exact. It approximates to

57+7*sqrt(3) = 69.12435565

The units for the perimeter are in kilometers, and you won't have any exponent over the "km". While your teacher doesn't want the units, it's still handy to know what the units would be.

larisa86 [58]2 years ago
5 0

Step-by-step explanation:

solution given:

for rectangle

length [l]=18km

breadth [b]=7√3 km

for triangle

base[b1]=25-18=7km

height [h]=b=7√3km

for area :area of. (rectangle +triangle}=

l×b+1/2 b1×h=18×7√3+1/2 ×7×7√3=260.67km²

now

perimeter=sum of all sides

=18+14+25+7√3=69.12km

is your answer

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