Question

I will mark the Brainliest answer. Please Help me! :)
How does the area of triangle ABC compare to the area of parallelogram GHJK?


A. The area of △ABC is 2 square units greater than the area of parallelogram GHJK.

B. The area of △ABC is 1 square unit greater than the area of parallelogram GHJK.

C. The area of △ABC is equal to the area of parallelogram GHJK.

D. The area of △ABC is 1 square unit less than the area of parallelogram GHJK.

Answer 1

Given :

A parallelogram JKGH where ,

J(-2,4) , K ( -3,2) , G (0,0) , H ( 1,2)

A triangle ABC where ,

A( 2,0) , B (1,-6) , C (-2,-4)

To Find :

which of the following is correct

A. The area of △ABC is 2 square units greater than the area of parallelogram GHJK.

B. The area of △ABC is 1 square unit greater than the area of parallelogram GHJK.

C. The area of △ABC is equal to the area of parallelogram GHJK.

D. The area of △ABC is 1 square unit less than the area of parallelogram GHJK.

Solution:

•Area of triangle with its coordinates as (x1,y1) , (x2,y2) ,(x3,y3) is

Area = 1/2 [ x1(y2-y3) + x2(y3-y1) + x3(y3-y1) ]

•Now , Area of triangle ABC is

A = 1/2| [2(-6+4) + 1( -4-0) +(-2)(0+6)] |

A = 1/2 | [ 2(-2) + 1(-4) + (-2)(6) ] |

A = 1/2| [ -4 - 4 - 12 ] |

A = 1/2| [ -20 ] |

A = | -10 | = 10

Area of triangle ABC = 10 sq units

•Now ,

Area of parallelogram JKGH = Area of triangle JHG + Area of triangle JKG

•Area of triangle JHG is

A = 1/2 | [ -2(2-0) + 1(0-4) + 0(4-2) ] |

A = 1/2 | [ -4 -4 ] |

A = 1/2 |-8| = |-4| = 4 sq units

•Area of triangle JKG is

A = 1/2 | [ -2(2-0) + -3(0+2) + 0(4-2) ] |

A = 1/2 | [ -4 - 6 ] |

A = 1/2 | -10 |

A = |-5| = 5 sq . units

•Area of parallelogram JKGH is 9 sq.units

•Hence , The area of △ABC is 1 square unit greater than the area of parallelogram JKGH.

•So, option B is correct