Answer to Question #198682 in Geometry for Nonkululeko

Question

The net of a pyramid is seen as a square at the base with four triangles attached to the square. Each triangular side has an area which exactly half of the erea of the square base. What fraction of the total area of the net is taken up by the base?

Answer 1

Let,

$A =$ Total Area

$A_1 =$ Area of one triangle

$A_2 =$ Area of square

We have given that,

$A_1 = \dfrac{1}{2}A_2$

Hence,

$4A_1 = 2A_2$

Total area $A = 4A_1+A_2$

$A= 3A_2$

Hence, $A_2= \dfrac{1}{3}A$