The four sequential sides of a quadrilateral have lengths a = 5.7, b = 8.3, c = 10.2, and d = 11.6 (all measured in yards). The angle between the two smallest sides is a = 107°. What is the area of this figure? area = yd² Question Help: Video Post to forum Submit Question
The four sequential sides of a quadrilateral have lengths a = 5.7, b = 8.3, c = 10.2, and d = 11.6 (all measured in yards). The angle between the two smallest sides is a = 107°. What is the area of this figure? area = yd² Question Help: Video Post to forum Submit Question
Calculus: Early Transcendentals
8th Edition
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Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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![**Calculating the Area of a Quadrilateral**
The four sequential sides of a quadrilateral have lengths \(a = 5.7\), \(b = 8.3\), \(c = 10.2\), and \(d = 11.6\) (all measured in yards). The angle between the two smallest sides is \(\alpha = 107^\circ\).
What is the area of this figure?
**Enter your answer:**
- **Area:** \(\_\_\_\_\_\_\_\_\) yd²
**Question Help:**
- [Video]
- [Post to forum]
**Submit Question**
---
Explanation:
To calculate the area of a quadrilateral given the lengths of its sides and one angle, you can use the formula for the area of a cyclic quadrilateral (a quadrilateral that can be inscribed in a circle) and correct it if the quadrilateral is not cyclic.
In this scenario, the quadrilateral’s sides and the angle are:
- \(a = 5.7\)
- \(b = 8.3\)
- \(c = 10.2\)
- \(d = 11.6\)
- \(\alpha = 107^\circ\)
By applying Brahmagupta's formula for a cyclic quadrilateral or Heron's formula, considering possible corrections of non-cyclic quadrilateral involving trigonometric functions, you can determine the area.
Use the appropriate detailed mathematical procedure to find the area in square yards. For further assistance, you can watch the linked video or post the question in the forum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd214627-2ece-4863-8550-f4375b9de9e0%2F5725c174-f20f-4f70-9ae2-2406404af858%2F4jpttp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Calculating the Area of a Quadrilateral**
The four sequential sides of a quadrilateral have lengths \(a = 5.7\), \(b = 8.3\), \(c = 10.2\), and \(d = 11.6\) (all measured in yards). The angle between the two smallest sides is \(\alpha = 107^\circ\).
What is the area of this figure?
**Enter your answer:**
- **Area:** \(\_\_\_\_\_\_\_\_\) yd²
**Question Help:**
- [Video]
- [Post to forum]
**Submit Question**
---
Explanation:
To calculate the area of a quadrilateral given the lengths of its sides and one angle, you can use the formula for the area of a cyclic quadrilateral (a quadrilateral that can be inscribed in a circle) and correct it if the quadrilateral is not cyclic.
In this scenario, the quadrilateral’s sides and the angle are:
- \(a = 5.7\)
- \(b = 8.3\)
- \(c = 10.2\)
- \(d = 11.6\)
- \(\alpha = 107^\circ\)
By applying Brahmagupta's formula for a cyclic quadrilateral or Heron's formula, considering possible corrections of non-cyclic quadrilateral involving trigonometric functions, you can determine the area.
Use the appropriate detailed mathematical procedure to find the area in square yards. For further assistance, you can watch the linked video or post the question in the forum.
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