Calculating Areas of Triangles

The video tutorial explains how to find the area of a quadrilateral with given side lengths and an angle between the two smallest sides. The quadrilateral is divided into two triangles, and the area of each triangle is calculated separately. The first triangle's area is found using the sine formula, while the second triangle's area is determined using Heron's formula. The law of cosines is applied to find a missing side length. Finally, the areas of the two triangles are summed to find the total area of the quadrilateral.

What is the angle between the two smallest sides of the quadrilateral?

• 120 degrees

• 45 degrees

• 90 degrees

• 107 degrees

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CCSS.HSG.SRT.D.9

Which formula is used to calculate the area of the first triangle?

• Cosine formula

• Heron's formula

• Pythagorean theorem

• Sine formula

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CCSS.6.G.A.1

What is the approximate area of the first triangle?

• 25.3 square meters

• 30.1 square meters

• 16.5 square meters

• 20.5 square meters

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which law is used to find the missing side length in the second triangle?

• Law of Sines

• Law of Cosines

• Law of Tangents

• Law of Secants

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the approximate length of the missing side found using the law of cosines?

• 8.5 meters

• 10.2 meters

• 11.3 meters

• 9.75 meters

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CCSS.HSG.SRT.D.9

What is the semi-perimeter used in Heron's formula for the second triangle?

• 16.2

• 13.9

• 14.5

• 15.8

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CCSS.6.G.A.1

What is the approximate area of the second triangle?

• 50.2 square meters

• 44.5 square meters

• 39.8 square meters

• 48.1 square meters

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CCSS.6.G.A.1

What is the total area of the quadrilateral?

• 70.5 square meters

• 65.2 square meters

• 61.07 square meters

• 55.3 square meters

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CCSS.3.MD.C.7D

Which method is used to find the total area of the quadrilateral?

• Dividing the areas of two triangles

• Multiplying the areas of two triangles

• Adding the areas of two triangles

• Subtracting the areas of two triangles

What is the purpose of dividing the quadrilateral into two triangles?

• To simplify the calculation of the area

• To determine the height

• To find the perimeter

• To calculate the volume