Find the area of quadrilateral ABCD.

Mathematics

2 answers:

maria [59]4 years ago

8 0

The correct answer is B. 14.89 units squared.

Find the area of each triangle and add them together. Heron’s formula explains it better than me. Lol

nalin [4]4 years ago

3 0

Answer:

<h2> 14.89 units²</h2>

Step-by-step explanation:

$P_{ABCD}=P_{ACD}+P_{ABD}$

We can use Heron's formula to calculate area of triangles:

$P_\triangle=\sqrt{s(s-a)(s-b)(s-c)}$ where:

a, b, c - sides of triangle

s - semi-perimetr of triangle {(a+b+c):2}

ΔACD:

a = 4.39 , b = 3.42 , c = 4.57

s = (4.39 + 3.42 + 4.57)÷2 = 12.38÷2 = 6.19

$P_{ACD}=\sqrt{6.19(6.19-4.39)(6.19-3.42)(6.19-4.57)}\\\\P_{ACD}=\sqrt{6.19\cdot1.8\cdot2.77\cdot1.62}=\sqrt{49.9986108}=7.070969579...\\\\P_{ACD}\approx7.071$

ΔACD:

a = 5.44 , b = 7.84 , c = 3.42

s = (5.44 + 7.84 + 3.42)÷2 = 16.7÷2 = $P_{ACD}=\sqrt{8.35(8.35-5.44)(8.35-7.84)(8.35-3.42)}\\\\P_{ACD}=\sqrt{8.35\cdot2.91\cdot0.51\cdot4,93}=\sqrt{61.09371855}=7.81624708...\\\\P_{ACD}\approx7.816$