Question

Jeremy makes a paperweight for his mother in the shape of a square pyramid. The base of the pyramid

has a side length of 10 centimeters, and the lateral faces have heights of 11 centimeters. After he finishes,
he realizes that the paper weight is too small and decides to make another one. To make the second
pyramid, he doubles the length of the base in the first pyramid.
Select Yes or No to indicate whether the statement is correct.
?
The surface area of the second pyramid is 840 cm?.
The surface area doubled from the first pyramid to the second pyramid.
?
The lateral area doubled from the first pyramid to the second pyramid.
2​

Answer 1

TRUE-The surface area of the second pyramid is 840 .

FALSE-The surface area doubled from the first pyramid to the second pyramid.

TRUE-The lateral area doubled from the first pyramid to the second pyramid.

Explanation:

First Pyramid

Side length of the base of the square pyramid = 10 centimeters

Heights of the lateral faces = 11 centimeters.

Lateral Area of the First Pyramid
`=4(\frac12 * 10 *11)=220$ cm^2`

Surface Area of the first Pyramid =Base Area + Lateral Area

`=10^2+220\\=320$ cm^2`

Second Pyramid

Side length of the base of the square pyramid = 2*10=20 centimeters

Heights of the lateral faces = 11 centimeters.

Lateral Area of the second Pyramid
`=4(\frac12 * 20 *11)=440$ cm^2`

Surface Area of the second Pyramid =Base Area + Lateral Area

`=20^2+440\\=840$ cm^2`

From the above,

• The lateral area doubled from the first pyramid (220) to the second pyramid(440).

Also,

• The surface area of the second pyramid is 840 square centimeter.

This statement is however false:

• The surface area doubled from the first pyramid to the second pyramid.