Question

if a triangle and s square are on the same base and between the same parallels then the ratio of area of triangle to the area of square is:

Answer 1

Refer to the attached image.

Since, the triangle and  square are on the same base AB and between the same parallels AB and CD.

We have to find the ratio of area of triangle to the area of square.

Area of triangle with base 'b' and height 'h' is given by $\frac{1}{2} \times b \times h$

Area of square with side 's' is given by $s \times s$

Area of triangle = $\frac{1}{2} \times AB \times EF$

= $\frac{1}{2} \times a \times a$

= $\frac{1}{2} \times a^2$

= $\frac{a^2}{2}$ square units.

Area of square = AB $\times CB$

= $a \times a$

= $a^2$ square units.

Now, let us find the ratio of area of triangle to the area of square

= ${\frac{a^2}{2}} \div a^2$

= $\frac{1}{2}$

= 1:2

Hence, the ratio of area of triangle to the area of square is 1:2.