Question

The area of isosceles triangle XYZ with two equal sides XY and XZ as 5cm each and YZ as 8cm is________.​

Answer 1

Answer:

12 $cm^{2}$

Step-by-step explanation:

ISOSCELES TRIANGLE:

• In an isosceles triangle, the two opposite sides are equal in length.
• The unequal side of an isosceles triangle is called base of the triangle.
• The base angles in an isosceles triangle is equal.
• Altitude is the median drawn from the apex angle.
• The altitude of an isosceles triangle bisects the base into two equal parts and the triangle is divided into two equal right angled triangles.

Area of isosceles triangle = $\frac{1}{2}$ × base×altitude

Since, the altitude divide the base into equal parts and triangle into two right angled triangles; the height can be found by:

$h^{2} + 4^{2} = 5^{2} \\\\h^{2} = 25-16\\\\h^{2} = 9$

h = 3 cm

Area of isosceles triangle = $\frac{1}{2}$ × base×altitude

$= \frac{1}{2}$ ×8 × 3

= 12

Area = 12 $cm^{2}$

To know more about isosceles triangle visit the link given below:

https://brainly.in/question/1079349

To know how to find the area of a triangle visit the link below:

https://brainly.in/question/7808869

Answer 2

Answer:

The area of the triangle = 12cm²

Step-by-step explanation:

Given,

The equal sides of an isosceles triangle XY = YZ = 5cm

The base of the isosceles triangle = 8cm

To find,

The area of the isosceles triangle

Solution:

Recall the concepts:

The area of a triangle = $\frac{1}{2}$× base× height

The altitude of an isosceles triangle passes through the midpoint of the base

Pythagoras theorem:

The hypotenuse of a right-angled triangle is equal to the sum of squares of the other two sides.

Let us draw an altitude of the triangle from the vertex X to meet the the bas YZ and P.

The area of the triangle  $\frac{1}{2}$× base× height =  $\frac{1}{2}$× YZ× XP

To find the length of the height of the triangle XP

Since the altitude of an isosceles triangle passes through the midpoint of the base, we have P is the midpoint of the side YZ

XP = YP = 4cm

And also ΔXPY is a right-angled triangle, right-angled at P, and hypotenuse XY

Then by Pythagoras theorem, we have

XY² = YP² + XP²

5² = 4² + XP²

25 = 16+XP²

XP² = 25-16 = 9

XP = 3

The height of the triangle = 3cm

Hence the area of the triangle =  $\frac{1}{2}$× base× height =  $\frac{1}{2}$× YZ× XP

=   $\frac{1}{2}$×8×3 = 12cm²

The area of the triangle = 12cm²

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