Question

Find the area of a quadrilateral ABCD having vertices at A(1, 2),
B(1,0), C(4,0) and D(4,4).​

Answer 1

Step-by-step explanation:

Given Find the area of a quadrilateral ABCD having vertices at A(1, 2),

B(1,0), C(4,0) and D(4,4).

• Let the points be A(1,2), B(1,0), C(4,0) and D(4,4)
• The quadrilateral ABCD can be divided into two triangles ABC and ACD and sum of these two triangles is the area of the quadrilateral.
• So   Area of triangle with vertices (x1,y1); (x2,y2) and (x3,y3) is  
• l x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2) / 2 l
• l 1(0 – 0) + 1(0 – 2) + 4(2 – 0) / 2 l
• l 0 – 2 + 8 / 2 l
• = 6/2
• = 3
• Now for area of triangle ACD is  
• So x1(y3 – y4) + x3 (y4 – y1) + x4(y1 – y3)
•  So  l  1(0 – 4) + 4 (4 – 2) + 4(2 – 0) l
• So l – 4 + 8 + 8 / 2 l
•   = 12 /2  
• = 6

Therefore area of the quadrilateral will be 3 + 6 = 9 sq units

Reference link will be

https://brainly.in/question/15922782

Answer 2

The area of a quadrilateral ABCD having vertices at A(1, 2),  B(1,0), C(4,0) and D(4,4) is 15 sq.units.

Given,

A(1, 2),  B(1,0), C(4,0) and D(4,4).​

Area of quadrilateral = 1/2 × { ( x1y2 +x2y3 + x3y4 + +x4y1) - (x2y1 + x3y2 + x4y3 + x1y4) }

= 1/2 × { ( 1×0 + 1×0 + 4×4 + 4×2) + ( 1×2 + 4×0 + 4×0 + 1×4) }

= 1/2 × { 16 + 8 } + { 2 + 4 }

= 1/2 × {24 + 6 }

= 1/2 × 30

= 15 sq.units