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levacccp [35]
4 years ago
13

Find the lateral area of the pyramid to the nearest whole number.

Mathematics
1 answer:
son4ous [18]4 years ago
7 0

Answer:

The correct answer is first option.  204 m²

Step-by-step explanation:

Formula:-

Lateral surface area of square pyramid = 4 * area  of triangle

<u>To find the slant height of triangle(l)</u>

l = √(6² + 6²) = 6√2

To find the area of triangle

Area = bh/2

b = 12 m

h =  6√2

Area = (12 * 6√2)/2 = 36√2

<u>To find the lateral surface area of Prism</u>

Lateral surface area of square pyramid = 4 * area  of triangle

= 36√2 * 4 = 203.64 ≈ 204 m²

First answer is the correct option

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2 years ago
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A rectangular field on a farm is to be fenced in using the wall of the barn for one side and 200 meters of fencing for the other
vitfil [10]

Answer:

Rectangular area as a function of x :   A(x)  = 200*x  + 2*x²

A(max) = 5000 m²

Dimensions:

x = 50 m

l  = 100 m

Step-by-step explanation:

"x" is the length of the perpendicular side to the wall of the rectangular area to be fenced, and we call "l" the other side (parallel to the wall of the barn) then:

A(r) = x* l     and the perimeter of the rectangular shape is

P = 2*x + 2*l   but we won´t use any fencing material along the wll of the barn therefore

P  =  2*x + l       ⇒   200 = 2*x  + l      ⇒   l  = 200 - 2*x      (1)

And the rectangular area as a function of x is:

A(x)  = x * ( 200 - 2*x)  ⇒  A(x)  = 200*x  + 2*x²

Taking derivatives on both sides of the equation we get:

A´(x)  =  200 - 4*x     ⇒   A´= 0

Then    200 - 4*x  = 0     ⇒   4*x =  200   ⇒  x  = 50 m

We find the l value, plugging the value of x in equation (1)

l  = 200 - 2*x     ⇒ l = 200 - 2*50   ⇒  l = 100  m

A(max)  =  100*50

A(max)  = 5000 m²

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