Question

Answer correctly.
Geometry: Parallelogram Proofs

Answer 1

3. GK = 9 cm

4. A = 4√65 cm^2

Explanation:

Given:

Rectangle FGHK

FH = 9 cm

FG = 4 cm

Find: GK - ?, A (area) - ?

3. Diagonals of a rectangle are of equal length

FH = GK = 9 cm

4. We need to find the longer side length of the triangle (we can use the Pythagorean theorem from ∆FGH or ∆FHK, since they are right triangles):

`{gh}^(2) = {fh}^(2) - {fg}^(2)`

`{gh}^(2) = {9}^(2) - {4}^(2) = 81 - 16 = 65`

`gh > 0`

`gh = √(65) \: cm`

Now, we can find the area:

`a = √(65) * 4 = 4 \sqrt{65 \: {cm}^(2) }`