Question

find the area of a rhombus if its vertices are (3,0),(4,5),(-1,4)and (-2,-1)taken in ordering

Answer 1

Step-by-step explanation:

1. Consider the four points as the vertices of the rhombus
2. Take three points at a time that form a triangle
3. Calculate the area of this triangle by the fornula A=1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2) where(x1,y1),(x2,y2) and (x3,y3) are the points respectively.
4. Similarly do it for the adjacent triangle.
5. Dont worry if the answer is negative just take its positive one(modulus)
6. add the two areas

Answer 2

Answer:

=> A(3,0) , B(4,5) , C(-1,4) , D(-2,-1)

ABCD IS A RHOMBUS

=> AREA OF RHOMBUS ==> 1/2 * AC * BD

=> DISTANCE B/W AC

=> AC² = (3+1)²+(0-4)²

=> AC² = 16 + 16

=> AC² = 32

=> AC = √32 ==> 4√2 UNIT

NOW, DISTANCE BETWEEN BD

=> BD² = (4+2)²+(5+1)²

=> BD² = 36+36

=> BD = √72

=> BD = 6√2 CM

AREA OF RHOMBUS ==> 1/2×AC×BD

=> 1/2×4√2×6√2

=> 2√2 × 6√2

=> 24 CM

AREA = 24 CM