Triangles Unit Test
Math 8 Q2 (Pre-Algebra) / Triangles
find the slant height of the square pyramid (1 point) solve
12cm
4cm
3cm
To find the slant height of the square pyramid, we need to use the Pythagorean Theorem. The slant height is the hypotenuse of a right triangle formed by one of the triangular faces of the pyramid and the height of the pyramid.
Let the base side length of the square pyramid be represented by "x".
Using the Pythagorean Theorem, we have:
(x/2)^2 + 3^2 = slant height^2
(x^2/4) + 9 = slant height^2
To find the value of "x", we can use the fact that the base of the pyramid is a square. In a square, all the sides are equal. Therefore, x = 12 cm.
Substituting this value into the equation:
(12^2/4) + 9 = slant height^2
144/4 + 9 = slant height^2
36 + 9 = slant height^2
45 = slant height^2
Taking the square root of both sides, we get:
slant height = √45 cm
Simplifying this, we have:
slant height ≈ 6.71 cm
Therefore, the slant height of the square pyramid is approximately 6.71 cm.