The area enclosed by the graphs of $|x + y| = 2$ and $|x| = 1$ is

Let $\alpha, \beta, \gamma, \delta \in \mathbb{Z}$ and let $A(\alpha, \beta), B(1, 0), C(\gamma, \delta)$ and $D(1, 2)$ be the vertices of a parallelogram $ABCD$. If $AB = \sqrt{10}$ and the points $A$ and $C$ lie on the line $3y = 2x + 1$,then $2(\alpha + \beta + \gamma + \delta)$ is equal to

$A$ farmer owns a triangular plot in Guntur. He measures the lengths of the sides of his property as $4 \text{ cm}$,$5 \text{ cm}$,and $7 \text{ cm}$. Then the area of land of the farmer in $\text{sq. cm}$ is

Let $A(-2,-1)$,$B(1,0)$,$C(\alpha, \beta)$,and $D(\gamma, \delta)$ be the vertices of a parallelogram $ABCD$. If the point $C$ lies on $2x-y=5$ and the point $D$ lies on $3x-2y=6$,then the value of $|\alpha+\beta+\gamma+\delta|$ is equal to . . . . . . .

The coordinates of the feet of the perpendiculars from the vertices of a triangle to the opposite sides are $(20, 25)$,$(8, 16)$,and $(8, 9)$. Find the orthocenter of the triangle.

For what value of $y$ does the triangle with vertices $A(2, 7)$,$B(4, y)$,and $C(-2, 6)$ form a right angle at $A$?