Since we cannot draw the figure here, you can draw the figure yourself.
Note that a right pyramid is a pyramid with a square base and the apex (the tip of the pyramid) is aligned directly at the center of the base.
Now, draw an line from the apex to the center of the base, which serves as the height of the pyramid. Then connect the center of the base to one of the midpoints of the side of the square. The slant height is from that midpoint to the apex.
Note that you have formed a right triangle, where the height is unknown, and the hypotenuse (which is also the slant height) is 15 cm. You can solve for the base of the right triangle by getting the half of the side of the square, which is 6 cm.
Solving for height, recall pythagorean theorem. For any right triangle,
a^2 + b^2 = c^2
a = base of right triangle
b = height of right triangle
c = hypotenuse
6^2 + b^2 = 15^2
36 + b^2 = 225
b^2 = 189
b = 3*sqrt(21) cm [height]
Recall that the volume of ANY pyramid is just
V = (Area of the base)*(height)/3
*Area of the base = (length of side of square)^2
V = (12^2)*[3*sqrt(21)]/3
V = 144*sqrt(21) cm^3
Recall that the SA of a SQUARE pyramid is just
SA = 2bs + b^2
s = slant height
b = length of side of square
SA = 2*12*15 + 12^2
SA = 504 cm^2
Hope this helps~ :)
Maths - OPQRS is a right pyramid whose base is a square of sides 12cm each. ...
Mathematics - OPQRS is a right pyramid whose base is a square of sides 12cm each...
MATH! PLEASE REPLY ASAP! - OPQRS is a regular square-pyramid whose base has ...
Maths - Solve the equation:a right pyramid with vertical height stand on ...
Maths - A right pyramid on a base 4cm square has a slant edge of 6cm.calculate ...
GEOMETRY - FIND THE LATERAL AREA OF A RIGHT PYRAMID WHOSE SLANT HEIGHT IS 18mm ...
Geometry - Determine the slant height of a right pyramid whose lateral area is ...
geometry - Determine the slant height of a right pyramid whose lateral area is ...
Geometry - The base of a regular pyramid is a hexagon whose sides have length 5 ...
math - The base of a regular pyramid is a square whose sides have a length 8 cm...