Question

What is the area of rhombus ABCD? Enter your answer in the box. Do not round at any steps.

Answer 1

Answer:

16 square units.

Step-by-step explanation:

We know that any diagonal of a rhombus divides the rhombus into two equal parts having the same area.

Now. the area of Δ ABC can be calculated from the coordinates of its three vertices.

Here, A(-1,4), B(3,2) and C(-1,0) are given.

Hence, the area of Δ ABC will be  

$\frac{1}{2} |-1(2-0)+3(0-4)-1(4-2)|= \frac{1}{2}|-2-12-2|= 8$ square units.

Therefore, area of the rhombus will be (8 × 2) = 16 square units. (Answer)

Note: If the three vertices of a triangle ABC are given to be (x1,y1), (x2,y2), and (x3,y3), then area of the triangle will br given by  

$\frac{1}{2} |x1(y2-y3) +x2(y3-y1)+ x3(y1-y2))|$.