The scale of a map is 5 cm : 1 km. A reservoir has an actual area of $0.7\text{ km}^2$. Find the area, in square centimetres, of the reservoir on the map. Answer ... $\text{cm}^2$ $ABCD$ is a rhombus. $X$ and $Y$ are points on $BD$ such that $DX = YB$. Show that triangle $ADX$ is congruent to triangle $ABY$. Give a reason for each statement you make. Answer

1. Find the area scale factor from the linear scale.

Linear scale is $5\text{ cm} : 1\text{ km}$.
Area scale is $(5\text{ cm})^2 : (1\text{ km})^2$
$25\text{ cm}^2 : 1\text{ km}^2$

2. Calculate the map area for the given actual area.

Actual area = $0.7\text{ km}^2$
Map area = $0.7 \times 25 = 17.5\text{ cm}^2$

1. State the equality of the sides of the rhombus

$AD = AB$ (sides of a rhombus are equal)

2. State the equality of the angles bisected by the diagonal

$\angle ADX = \angle ABY$ (diagonal of a rhombus bisects the interior angles, or base angles of isosceles triangle $ABD$)

3. State the given equality of the segments on the diagonal

$DX = YB$ (given)

4. Conclude congruence using SAS

Therefore, triangle $ADX$ is congruent to triangle $ABY$ (SAS).