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

Question

https://dw6y82u65ww8h.cloudfront.net/organisations/48/HSCC_Geom_01.04.17.png pleae use the link and help me out. I am having some trouble.

Answer 1

Pythagoras!

AD² = 9² + 9²

AD = 9√2

BC² = 4² + 4²

BC = 4√2

FB² = 2² + 2²

FB = 2√2

Now use formula for area of trapezoid

A = (0.5)(b₁ + :b₂)(h)

Answer 2

Since there is exactly one pair of parallel sides, the figure is a trapezoid and we can use the formula:

A = ¹/₂(b₁ + b₂)h

b₁ = AD = √((x₂ - x₁)² + (y₂ - y₁)²) = √((4 - (-5))² + ((-5) - 4)²) = √((-9)² + (-9)²) = √(81 + 81) = √(2*81) = 9√2

b₂ = BC = √((x₂ - x₁)² + (y₂ - y₁)²) = √((4 - 0)² + ((-1) - 3)²) = √((4)² + (-4)²) = √(16 + 16) = √(2*16) = 4√2

h = FB = √((x₂ - x₁)² + (y₂ - y₁)²) = √(((-2) - 0)² + (1 - 3)²) = √((-2)² + (-2)²) = √(4 + 4) = √(2*4) = 2√2

A = ¹/₂(b₁ + b₂)h

A = ¹/₂(9√2 + 4√2)(2√2)

A = ¹/₂(13√2)(2√2)

A = ¹/₂(26)(2)

A = 26

Answer 3

draw right triangles and use the Pythagorean Theorem to find AF, FE and ED

once you find ED, you can find EC (and also FB)

AF=3√2, FE=4√2, ED=2√2, EC=2√2

now you can find the area of both triangles and the rectangle

you could have also used the distance formula to find the lengths you needed

you can do the math to find the area