Question

Find the area of quadrilateral with vertices at points (3,0)(4,5)(-1,4)(-2,-1)

Answer 1

Step-by-step explanation:

$Let the points be A(3,0),B(4,5),C(−1,4) and D(−2,−1)Area of a rhombus =21×(diagonal1×diagonal2)Hence, the distance between the points A(3,0) and C(−1,4)=(−1−3)2+(4−0)2=16+16=32And, Distance between the points B(4,5) and D(−2,−1)BD=(−2−4)2+ (−1−5)2=36+36=72So, Area of the rhombus =21×32×72=21×32×72=21×4×8×36×2=21×2×68×2=62×4×2=6×2×2=24 sq units$

Answer 2

Answer: 20

Step-by-step explanation:

Let 's complete our quadrilateral to a rectangle ; and subtract from it the area highlighted in red

$\displaystyle \rm S_{\diamond}=6\cdot 5 =30 \\\\ S_{ABCD}=30-(5:2+5:2+5:2+3:2+1\cdot1)=30-(7,5+1,5+1)=\\\\30-10=20 \\\\ S_{ABCD}=20$