In a given square $A B C D$ , if the area of triangle $A B D$ is $36 c m^{2}$ , find
(i) the area of triangle $B C D$ ; (ii) the area of the square $A B C D$

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Solution

$A B C D$ is a square
$B D$ is the diagonal
We know that the diagonal divides the square into two congruent triangles.
$∴$ $△ A B D$ $≅ △ B C D$
$∴$ Area of $△ A B D$ =area of $△ B C D$
Area of $△ A B D$ = $36 c m^{2}$ (given)
$∴$ Area of $△ B C D$ = $36 c m^{2}$
Area of the square $A B C D$ = Area of $△ A B D$ + Area of $△ B C D$ = $36 c m^{2}$ + $36 c m^{2}$
Area of the square $A B C D$ = $72 c m^{2}$

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In a given square ABCD, if the area of triangle ABD is 36 cm2, find(i) the area of triangle BCD; (ii) the area of the square ABCD

In a given square $A B C D$ , if the area of triangle $A B D$ is $36 c m^{2}$ , find
(i) the area of triangle $B C D$ ; (ii) the area of the square $A B C D$