Question

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Answer 1

Answer:

Step-by-step explanation:

1) Diagonal bisect the angles of Rhombus

∠CAB = ∠CAD

∠CAB = 71

2) ∠DAB = ∠CAB + ∠CAD

 ∠DAB = 71 + 71 = 142

In Rhombus, adjacent angles are supplementary

∠DAB + ∠ABC = 180

142 + ∠ABC = 180

           ∠ABC = 180 - 142

         ∠ABC = 38

3)  In rhombus, opposite angles are congruent

∠ADC = ∠ABC

∠ABC = 38

In rhombus, diagonal bisect angles

∠BDC = (1/2)*∠ADC

∠BDC= 38/2

∠BDC = 19

4) Diagonals bisect each other at 90

∠DEC = 90

5) Diagonals bisect each other

BE = DE

BE + DE = DB

7x -2 +7x -2 =24   {add like terms}

        14x - 4 =24

              14x = 24+4

              14x = 28

                 x = 28/14

                 x = 2 m

6) AB = 13m

BE = 7x - 2 = 7*2 -2 = 14 -2 = 12 m

In right angle ΔAEB,  {use Pythagorean theorem}

AE² + BE² = AB²

AE² + 12² = 13²

AE² + 144 = 169

         AE² = 169 - 144

         AE² = 25

         AE = √25

        AE = 5 m

Diagonals bisect each other

AE = EC

AC = 2*5

AC = 10 m

7)Side = 13 m

Perimeter = 4*side

                  = 4*13

 Perimeter = 52 m

8) d1 = AC = 10 m

   d2 = DB = 24 m

Area = $\frac{d_{1}*d_{2}}{2}$

         $=\frac{10*24}{2}$

          = 10 *12

          = 120 m²