Questions: 5. Find the area of the quadrilateral. Round to nearest square unit. Show work.

5. Find the area of the quadrilateral. Round to nearest square unit. Show work.
Transcript text: 5. Find the area of the quadrilateral. Round to nearest square unit. Show work.
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Solution

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Solution Steps

Step 1: Divide the quadrilateral into two triangles

The quadrilateral can be divided into two triangles by the diagonal of length 12. One triangle has sides of length 5, 12, and 16, and the included angle between sides 5 and 16 is 110°. The other triangle has sides of length 12, 12, and 16, and the included angle between the two sides of length 12 is unknown.

Step 2: Find the area of the first triangle

We can find the area of the first triangle using the formula Area = (1/2)ab_sin(C), where a and b are the lengths of two sides, and C is the angle between them. In this case, a = 5, b = 16, and C = 110°. So, Area1 = (1/2)_5_16_sin(110°) ≈ 37.6 square units.

Step 3: Find the area of the second triangle

The second triangle is an isosceles triangle with two sides of length 12. We can find the area of the second triangle using Heron's formula. First, calculate the semi-perimeter s: s = (12+12+16)/2 = 20. Then, the area is given by Area = sqrt(s(s-a)(s-b)(s-c)), where a, b, and c are the side lengths. Area2 = sqrt(20(20-12)(20-12)(20-16)) = sqrt(20_8_8*4) = sqrt(5120) ≈ 71.55 square units.

Step 4: Find the total area

The total area of the quadrilateral is the sum of the areas of the two triangles: 37.6 + 71.55 ≈ 109.15

Final Answer

109 square units

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