The measurements of the lateral surface of a square pyramid are shown in the figure. What are the slant height and the base edge of the pyramid respectively?

Open in App

Solution

By the angle sum property, it follows that the triangle is equilateral, and hence the base edge of the pyramid equals $20 c m$ .

Also, the triangle is isosceles implies that the altitude of the triangle face of the pyramid, or in other words the slant height of the pyramid bisects the base. $[1 m a r k]$

So, using Pythagoras theorem, the slant height of the triangle is
$\sqrt{20^{2} - 10^{2}} = \sqrt{300} = 10 \sqrt{3} c e n t i m e t r e s$ $[1 m a r k]$

Suggest Corrections

Similar questions

Q. Pyramid

A

and pyramid

B

are two square base pyramids. The base area of pyramid

A

4

times that of pyramid

B

. The lateral surface areas of the two pyramids are equal. Find the ratio of the slant height of pyramid

A

to the slant height of pyramid

B

Q. The angle opposite to the base edge of a square pyramid on its lateral face is 30

^{\circ}

. If the slant height of the pyramid is

20 c m

, what is the lateral surface area of the pyramid? (Note that

t a n 15^{\circ} = 0.268

)

Q. What is the total surface area of the square pyramid whose base edge is 6 cm long and the lateral faces are equilateral triangles?

The angle opposite to the base edge of a square pyramid on its lateral face is 30 $^{\circ}$ . If the slant height of the pyramid is 20 $c m$ , what is the lateral surface area of the pyramid? (Note that $t a n 15^{\circ} = 0.268$ )

In any square pyramid, the squares of the height, slant height and lateral edge are in arithmetic sequence.

Join BYJU'S Learning Program