Question

Find the area of rhombus JKLM given the coordinates of the vertices. Round to the nearest tenth if necessary.

J(-2, -4), K(2, 2), L(6, -4), M(2, -10)

Answer 1

• The area of rhombus JKLM is 48 units²

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Given

• Rhombus JKLM,
• Vertices at J(-2, -4), K(2, 2), L(6, -4), M(2, -10).

To find

• The area of rhombus JKLM

Solution

We know that diagonals of rhombus are perpendicular to each other.

Hence its area is half the product of diagonals.

The diagonals are JL and KM and one of them is vertical and the other one horizontal since x- or y-coordinates are equal in pairs.

Let's find the length of diagonals, using the difference of coordinates:

• JL = 6 - (-2) = 8 units,
• KM = 2 - (-10) = 12 units.

Now find the area:

• A = JL*KM /2 = 8*12 / 2 = 48 units²