The following picture is a square pyramid where DE=8 cm and m∠ADE=60°.
Find the surface area of the pyramid in both exact form and approximate form.
Round your approximate answer to one decimal place.
(Make sure you include formulas and numbers in the formulas as part of your solution.
Also include units in your final answers.)

Given:

The length of DE is 8 cm and the measure of ∠ADE is 60°.

We need to determine the surface area of the pyramid.

Length of AD:

The length of AD is given by

Length of AD = 8 cm

Slant height:

The slant height EF can be determined using the trigonometric ratio.

Thus, we have;

Thus, the slant height EF is 4√3

Surface area of the square pyramid:

The surface area of the square pyramid can be determined using the formula,

Substituting the values, we have;

The exact form of the area of the square pyramid is

Substituting √3 = 1.732 in the above expression, we have;

Rounding off to one decimal place, we get;

Thus, the area of the square pyramid is 174.8 cm²

174.9 cm²

Step-by-step explanation:

AD = 2 × (8cos60)

AD = 8

Base = 8²

= 64

4 triangles = 4(½ × 8 × 8sin60)

= 64sqrt(3)

SA = 64 + 64sqrt(3)

174.8512517

7

step-by-step explanation:

yuo ned the activity or vertical angle of the form of 1,7 but 2,2 has a c4,2 as it verticie so i not have a car

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕