A design for party favors are in the shape of a regular hexagonal pyramid. The hexagon has a side length of 6 inches. The lateral faces are isosceles triangles with equal sides of 9 inches.

The lateral area of the pyramid is:
A) 1082
B) 903
C) 965

And the base area is:
A) 362
B) 543
C) 245

Part 1)

Part 2)

Step-by-step explanation:

Part 1) Find the lateral area of the pyramid

we know that

The lateral area of the pyramid, is equal to the area of six congruent isosceles triangles

so

we have

Applying Pythagorean Theorem calculate the height of triangle

simplify

Find the lateral area

Part 2) Find the base area

we know that

The area of a regular hexagon is equal to the area of six equilateral triangles

so

Applying the law of sines to calculate the area of triangle

we have

substitute

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

95.03 is the answer. hope this !