Question

area of rectangle vertices are (-2,0), (5.0),(5,4),(-2,4)

Answer 1

Diagram in attachmemt.

$\:$

ANSWER :

$\:$

Area = 28 sq. units

$\:$

EXPLANATION :

$\:$

GIVEN :

$\:$

Four vertices of a rectangle are (-2,4) , (5,4) , (-2,0) , (5,0)

$\:$

FORMULA USED :

$\:$

$\sf \: area \: of \: a \: triangle= \frac{1}{2} |{x}_{1}({y}_{2} - {y}_{3}) + {x}_{2}({y}_{3} - {y}_{1}) + {x}_{3}({y}_{1} - {y}_{2} )|$

$\:$

SOLUTION :

$\:$

We know that the diagonal of a rectangle divides it into two equal triangles.

$\:$

So, area of △ABD = area of △BDC

$\:$

Area of △ABD

$\frac{1}{2} |( - 2)(4 - 0) + 5(0 - 4) + ( - 2)(4 - 4)|$

↬ $\frac{1}{2} |( - 2)(4) + 5( - 4) + ( - 2)(0)|$

↬ $\frac{1}{2} | - 8 - 20|$

↬ $\frac{1}{2} | - 28|$

↬ $\frac{1}{2} \times 28$

↬ $\sf \: 14 \: sq. \: units$

$\:$

Total area of rectangle

⇴ 2 × area of △ABC

⇴ ( 2 × 14 ) sq. units

⇴ 28 sq. units