The height of an isosceles triangle is 4 cm. Each of the two equal sides measure 5 cm. What is the area of the triangle?
Make a sketch and draw in the altitude.
See that right-angled triangle with hypotenuse 5 and height of 4 ?
You should recognize the 3-4-5 right-angled triangle, if not, use Pythagoras to find the base.
Area of triangle = (1/2)base x height
= (1/2)(6)(4) = .....
Good 👍
To find the area of the isosceles triangle, you can use the formula:
Area = (base * height) / 2
In this case, the height is given as 4 cm. However, we need to find the base of the triangle, which is also one of the equal sides.
Using the Pythagorean Theorem, we can calculate the base of the triangle:
c^2 = a^2 + b^2
where c is the hypotenuse, and a and b are the other two sides.
In our case, since the triangle is isosceles, the base is the same as the other two sides, so we can use the formula:
c^2 = 5^2 + 5^2
c^2 = 25 + 25
c^2 = 50
Taking the square root of both sides, we get:
c = √50
c ≈ 7.071 cm
Now that we have found the base, we can substitute the values into the area formula:
Area = (base * height) / 2
Area = (7.071 cm * 4 cm) / 2
Area = 28.284 cm²
Therefore, the area of the isosceles triangle is approximately 28.284 cm².
To find the area of an isosceles triangle, we can use the formula: Area = (base × height) / 2.
In this case, the height of the triangle is given as 4 cm. However, we need to determine the base length.
Since it is an isosceles triangle, it has two equal sides of 5 cm each. To find the base length, we can apply the Pythagorean theorem.
Let's call the base length of the triangle as 'b'. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse (the base of the triangle) is 'b', and the other two sides are 5 cm each. So, we can set up the equation as follows:
b^2 = 5^2 - 4^2
b^2 = 25 - 16
b^2 = 9
b = √9
b = 3 cm
Now, we have the base length (b = 3 cm) and the height (h = 4 cm). We can substitute these values into the area formula:
Area = (base × height) / 2
Area = (3 × 4) / 2
Area = 12 / 2
Area = 6 square cm
Therefore, the area of the isosceles triangle is 6 square cm.