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Area of A Triangle - Higher

The document explains the formula for calculating the area of a triangle using the formula Area = 1/2 * a * b * sin(C), where a and b are the lengths of two sides and C is the angle between them. It also provides examples of how to find the area when given the base and height, as well as how to solve for unknown lengths using the area formula. The document emphasizes the adaptability of the formula to different triangle configurations.

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21a.francis
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24 views1 page

Area of A Triangle - Higher

The document explains the formula for calculating the area of a triangle using the formula Area = 1/2 * a * b * sin(C), where a and b are the lengths of two sides and C is the angle between them. It also provides examples of how to find the area when given the base and height, as well as how to solve for unknown lengths using the area formula. The document emphasizes the adaptability of the formula to different triangle configurations.

Uploaded by

21a.francis
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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THE AREA OF A TRIANGLE = 1 𝑎𝑏 sin 𝐶

1 Check that you can:


The formula we know for the area of a triangle is
2 × 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡, where the height is always measured perpendicular to the base. • find the area of a triangle knowing its base and perpendicular height
Sometimes, we are not given the perpendicular height of a triangle. This would mean that we would not be able to calculate the area. • substitute into a formula
There is another formula we can use to calculate the area of a triangle. • change the subject of a formula.

For any triangle ABC: Example 1 Example 2


Calculate the area of the triangle below. The area of the triangle below is 16∙3 cm2. Calculate the length y.

The area of a triangle =


1 𝑎𝑏 sin 𝐶
2
This is a reverse problem. The lengths of the two sides either side of the angle
The formula requires the length of any two sides of a triangle along Area = 1 𝑎𝑏 sin 𝐶 measuring 82° are 4∙9 cm and y cm, so these are the values that need to be used
with the size of the angle that lies between the two sides. 2 in the formula.
We can adapt this formula to include the letters given in this
1
REMEMBER! The formula can be written in three ways: triangle, labelled PQR, and then use it to calculate the area. Area = 𝑎𝑏 sin 𝐶
2
Area =
1 𝑝𝑞 sin R
The area of a triangle = 1 𝑎𝑏 sin 𝐶 2 4∙9 × 𝑦 × sin 82°
2 16∙3 =
1
Area = × 5∙8 × 6∙7 × sin 135° 2
1
The area of a triangle = 𝑎𝑐 sin 𝐵 2
2 16∙3 × 2
Area = 13∙7 cm2 correct to 1 d.p. =y
1
The area of a triangle = 𝑏𝑐 sin 𝐴 4∙9 × sin 82°
2
y = 6∙7 cm correct to 1 d.p.

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