Find the area of quadrilateral ABCD. Round the area to the nearest whole number, if necessary.

Question

Answer 1

Use the distance formula to determine

Lengths of AF and BF then use area of triangle formula

Lengths of EC and ED then use area of triangle formula

Lengths of FE and BF then use area of parallelogram formula

Add the three areas.

Answer 2

BC is 4sqr2 in length, the hypotenuse of a right triangle with sides 4 and 4

AD is 9sqr2 in length, the hypotenuse of a right triangle with sides 9 and 9

average of BC and AD is half of 4sqr2+9sqr2 = 13sqr2/2

BR = 2sqr2 = the hypotenuse of a right triangle with sides 2 and 2

area = 13sqr2/2 x 2sqr2 = 13x2 = 26

Answer 3

You need the side measures.

With a graph, use the distance formula

given 2 points (x₁,y₁)and (x₂,y₂)

distance = √((x₂ - x₁)² + (y₂ - y₁)²)

AD = √((x₂ - x₁)² + (y₂ - y₁)²)

AD = √((-5 - 4)² + (4 - -5)²) = √162 = 9√2

BC = √((0 - 4)² + (3 - -1)²) = √32 = 4√2

BF = √((-0 - -2)² + (3 - 1)²) = √8 = 2√2

Now plug into the area formula for a trapezoid:

= 1/2 • (base1 + base2) • height

= 1/2 (9√2 + 4√2) • 2√2

= 1/2 (13√2) • 2√2

= 1/2 • 13 • 2 • √2 • √2

= 1/2 • 13 • 2 • 2

= 13 • 2

= 26