Question

Prove that in any square pyra-
mid, the squares of the height,
slant height and lateral edge are
in arithmetic sequence.
​

Answer 1

$\bold\red{ANSWER!!!}$

Side of the equilateral triangle = 30 cm

Side of the square = Side of the equilateral triangle = 30 cm

Area of the square = (side)2 = (30 cm)2 = 900 cm2

Area of one equilateral triangle =

$\frac{ \sqrt{3} }{4} {side}^{2}$

$= \frac{ \sqrt{3} }{4} \times {30 }^{2} \\ = 225 \sqrt{3}$

cm^2

Area of four equilateral triangles =

$225 \sqrt{3} \times 4 \\ = 900 \sqrt{3}$

cm^2

Surface area of the square pyramid = Area of square + Area of four equilateral triangles

= (900 + 900√3) cm2