Question

Find the area of quadrilateral ABCD. [Hint: the diagonal divides the quadrilateral into two triangles.]

A. 26.47 units²
B. 28.53 units²
C. 33.08 units²
D. 27.28 units²

Answer 1

B.) 28.53 units²

Explanation:

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Answer 2

Option B
`28.53\ units^(2)`

Explanation:

The area of quadrilateral ABCD is equal to the area of triangle ABD plus the area of triangle ADC

we know that

Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.

Let

a,b,c be the lengths of the sides of a triangle.

The area is given by:

`A=√(p(p-a)(p-b)(p-c))`

where

p is half the perimeter

`p=(a+b+c)/(2)`

step 1

Find the area of triangle ABD

we have

`a=AB=2.89\ units`

`b=BD=8.59\ units`

`c=DA=8.6\ units`

Find the half perimeter p

`p=(2.89+8.59+8.6)/(2)=10.04\ units`

Find the area

`A=√(10.04(10.04-2.89)(10.04-8.59)(10.04-8.6))`

`A=√(10.04(7.15)(1.45)(1.44))`

`A=√(149.89)`

`A=12.24\ units^(2)`

step 2

Find the area of triangle ADC

we have

`a=AC=4.3\ units`

`b=AD=8.6\ units`

`c=DC=7.58\ units`

Find the half perimeter p

`p=(4.3+8.6+7.58)/(2)=10.24\ units`

Find the area

`A=√(10.24(10.24-4.3)(10.24-8.6)(10.24-7.58))`

`A=√(10.24(5.94)(1.64)(2.66))`

`A=√(265.35)`

`A=16.29\ units^(2)`

step 3

Find the total area

`A=12.24+16.29=28.53\ units^(2)`