So we have 36 equal to one half times x times x times the sine of 30°. So what we can do now is we can use this area formula to solve for X because we know that area is equal to 36. See, well in this case we know that they're equal to each other and we don't know what they are. Well A would have to be are included angle. Well, you're also given a hint that the area for a isosceles triangles with two sides and included angle is equal to one half, B times C. So if this is triangles, I saw sally's, I can mark my two congruent sides And because 30° angles in between the two concurrent sides, this would be my 30° angle. Well let's go ahead and draw this triangle. Our ultimate goal is to find the perimeter. The formula for the area of an equilateral triangle is Area = √3/ 4 a 2, where a is the length of one of the sides.Īrea = √3/ 4 a 2 becomes Area = √3/ 4 × 8 2.So in this problem we're told that an isosceles triangle has a area of 36 m2 and we're told that in this isosceles triangle, there's a 30° angle in between the two congruent sides. Here is another method for calculating the area of an equilateral triangle. Heron’s formula for the area of an equilateral triangle is Area = √(s(s-a) 3), where a is the side length.įor a triangle that has 3 equal sides, the semi-perimeter is simply s = 3a/ 2. We will first look at finding the area of an equilateral triangle using Heron’s formula. Alternatively, Heron’s formula for an equilateral triangle is Area = √(s(s-a) 3), where a is the side length and s = 3a/ 2.Īn equilateral triangle is a triangle with 3 equal side lengths. The area of a triangle with 3 equal sides can be calculated with the formula Area = √3/ 4 a 2, where a is the length of one of the sides. How to Calculate the Area of a Triangle with 3 Equal Sides This is the same answer as before and either method can be used. This becomes Area = √35, which equals 5.92 cm 2. Here is an example of using the isosceles version of Heron’s formula: Area = √s(s-a) 2(s-b). The semi-perimeter is the sum of the sides divided by 2.Ģ + 6 + 6 = 14 and 14 ÷ 2 = 7. We can use the usual form of Heron’s formula to find the area. Heron’s formula for an isosceles triangle then becomes Area = √( s(s-a) 2(s-b) ), where a is the length of the two equal sides, b is the length of the other side and s = (2a + b) ÷ 2.įor example, here is Heron’s formula for an isosceles triangle with side lengths of 2 cm, 6 cm and 6 cm. For an isosceles triangle, two sides are the same length and we can say that side c = side a. Heron’s formula for any triangle is Area = √( s(s-a)(s-b)(s-c) ). Heron’s Formula for an Isosceles Triangle As long as the three side lengths are known, Heron’s formula works for all triangles. The advantage of Heron’s formula is that no other lengths or angles of the triangle need to be known. Heron’s formula allows us to calculate the area of a triangle as long as all 3 of its sides are known. The formula is named after Heron of Alexandria (10 – 70 AD) who discovered it. It can be used to calculate the area of any triangle as long as all three side lengths are known. Heron’s formula is Area = √( s(s-a)(s-b)(s-c) ), where a, b and c are the three side lengths of a triangle and s = (a + b + c) ÷ 2. This becomes Area = √(10 × 2 × 7 × 1), which simplifies to Area = √140.įinally, the square root of 140 is calculated using a calculator. We find the semi-perimeter by adding up the side lengths and dividing by 2.Ĩ + 3 + 9 = 20 and 20 ÷ 2 = 10. The semi-perimeter is simply half of the perimeter. The first step is to work out the semi-perimeter, s. It does not matter which sides are a, b or c.
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