OPQRS is a regular square-pyramid whose base has sides of 7 cm. Given that the total surface area of the pyramid is 161 cm2, find its slant height.
answer will be 8
Se the methos
H^2= B^2+P^2
You people are just desyroying the math. be ashame ofvyourself you cannot give correct answer of even 1 question shame on yourself
Ddfc
EXERCISE 7.2
To find the slant height of the square pyramid, we need to use the given information about its total surface area and the length of its base side.
The surface area of a regular square pyramid is given by the formula:
Surface Area = Base Area + 4 * (1/2 * Base Perimeter * Slant Height)
In this case, we are given the total surface area as 161 cm^2 and the length of the base sides as 7 cm. We need to solve for the slant height.
Step 1: Calculate the base area.
The base of the pyramid is a square, so its area equals the length of one side squared.
Base Area = Side length * Side length
Base Area = 7 cm * 7 cm
Base Area = 49 cm^2
Step 2: Calculate the base perimeter.
Since the base is a square, all sides are equal, so the perimeter can be found by multiplying the side length by 4.
Base Perimeter = Side length * 4
Base Perimeter = 7 cm * 4
Base Perimeter = 28 cm
Step 3: Substitute the values into the surface area formula and solve for the slant height.
161 cm^2 = 49 cm^2 + 4 * (1/2 * 28 cm * Slant Height)
161 cm^2 = 49 cm^2 + 56 cm * Slant Height
Rearrange the equation to solve for Slant Height:
112 cm * Slant Height = 161 cm^2 - 49 cm^2
112 cm * Slant Height = 112 cm^2
Divide both sides of the equation by 112 cm to isolate the slant height:
Slant Height = (161 cm^2 - 49 cm^2) / 112 cm
Slant Height = 112 cm^2 / 112 cm
Slant Height = 1 cm
Therefore, the slant height of the pyramid is 1 cm.
It's similar to the previous question.
Start with drawing a diagram if the book did not supply one.
O is the vertex of the pyramid.
Let D be the centre of the rectangle PQRS, and A=centre of side PQ.
OAD is a right triangle where OD is the height=h, and OA is the height of the slant face OPQ.
By Pythagoras theorem, we find
OA²=sqrt(OD²+AD²)
=sqrt(h²+3.5²)
Area of one slant face
=AQ*OA
=3.5sqrt(h²+3.5²)
Area of 4 slant faces
=14sqrt(h²+3.5²)
Area of rectangular base
=7*7
=49
Equate the sum of areas to total surface area
14sqrt(h²+3.5²)+49=161
Solve for h. I get 7.2 approx.