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Karolina [17]
3 years ago
11

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

Mathematics
2 answers:
marissa [1.9K]3 years ago
6 0

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

guapka [62]3 years ago
4 0

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

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The triangles are similar by SAS, so we can set up a proportion of their sides.

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