Answer:
1. [tex]150cm^{2}[/tex]
2. 29cm
3. ∠B = ∠D = 99°, ∠A = ∠C = 81°
4. x = 6cm, y = 4cm, DF = 20cm, EG = 16cm
Step-by-step explanation:
1. [tex]A=\frac{d_{1}d_{2}}{2} =\frac{15(20)}{2} =150cm^{2}[/tex]
2. [tex]A=\frac{d_{1}d_{2}}{2}[/tex]
[tex]d_{2}=\frac{2A}{d_{1}}=\frac{2(348)}{24} =29cm[/tex]
3. In a parallelogram, opposite angles are congruent; hence, ∠B = ∠D.
[tex]4x+15=6x-27[/tex]
[tex]2x=15+27[/tex]
[tex]x=21[/tex]
∠B = 4(21) + 15 = 99°
∠D = 6(21) - 27 = 99°
Also, consecutive angles are supplementary (their sum is equal to 180).
∠A + ∠B = 180
∠A = 180 - 99 = 81°
∠C = ∠A = 81°
4. In a parallelogram, diagonals bisect each other.
[tex]x+y=10[/tex] (Eq. 1)
[tex]2x-y=8[/tex] (Eq. 2)
Solve for x using either substitution or elimination. The variable y can be eliminated by adding the two equations.
[tex]3x=18[/tex]
[tex]x=6[/tex]
[tex]y=10-x=4[/tex]
After determining the values of x and y, find the length of DC and CG.
[tex]DC=x+y=6+4=10cm[/tex]
[tex]CG=2x-y=2(6)-4=8cm[/tex]
(Actually, there is no need to solve for DC and CG because it is equal to CF and CE, respectively.)
The lengths of the diagonals are
[tex]DF=10+10=20cm[/tex]
[tex]EG=8+8=16cm[/tex]
