Find the area. A isosceles triangle with base 10 and perimeter 36?

Question

May you show me how to get there?
Not the answer?

Answer 1

Perimeter = 36.units

Base = 10 units

Each of the two equal sides = (36- 10) / 2 = 26 / 2 = 13 units

Height of the Isoceles triangle = Root of (13 ^2) - (5 ^ 2)

= root of 12 ^2

= 12 units.

Area of the Triangle =1/2 * base & height

= 1/2 * 10 *12

= 60 sq. units. Answer.

Is it clear now?

If it is, give me my ten.

Answer 2

Hi. Let's give it a try...

Question: Find the area. A isosceles triangle with base 10 and perimeter 36?

Area of a triangle = 1/2 base X height

Isosceles = Two of the sides are the same (equivalent).

Base of an isoceles triangle = Not one of the equivalent sides; that is, the other side.

Perimeter = All of the sides added together. Triangles have three sides, as you know.

So then, the base is 10. That means that the other sides added together equal 26. Because 36 - 10 = 26.

So what is 26 divided by 2? That is how long each of the other sides are. 13.

Take that answer and plug it into the area formula at the top. Base (10 in this question) multiplied by 1/2 (0.5), multiplied by the height of the triangle, gives you the answer.

The question is, what is the height?

To find the height, use the Pythagorean Theorem:

A squared plus B squared equals C squared.

or A² + B² = C².

A and B are the 'legs' of the triangle, and C is the hypotenuse. The hypotenuse is the side adjacent to the right angle (90 degree angle) of the triangle.

Isosceles triangles have no hypotenuse, because they have no right angles. So we need a right triangle to use the Pythagorean Theorem.

Draw the isosceles triangle, if you haven't already. It should be a triangle with two sides the same and one side different. Like this:

http://www.nrich.maths.org.uk/content/id/2317/isosceleshalf3.png

Then create a right triangle by drawing a line through the middle of the triangle from the top of the triangle to the bottom. That 'side' that you just created is A, one of the legs.

Label each of the sides with the information you have. Remember, you're labeling the right triangle, not the isosceles triangle. A and B are the legs, and C is the hypotenuse. B will be half of 10, that is, 5. C is 13, as we said earlier.

Whew. Now you can use the Pythagorean Theorem.

A² + B² = C².

Square B and C, and you can find A. Then you'll know what the height of the triangle is and you can find the area.

B squared, 5² (5 X 5) is 25.

C squared, 13² (13 X 13) is 169.

So, A² + 25 = 169.

Simply subtract to find A².

169 - 25 = 144.

So A² is 144, and what number multiplied by itself gives you 144? 12.

So A is 12.

That means the height of the triangle is 12.

So let's go back to the formula one last time.

Area = 1/2 Base X Height

We already know that 1/2 of the Base is 5. We now know that the height, which we cleverly deduced by drawing an imaginary right triangle, is 12.

So, for the final answer, 5 multiplied by 12 is...

60!!

Area is always given in terms of squared units. If the question had used feet, inches, or centimeters, you would use those. For this question, there are no units given, so just write:

"60 units squared"

or "60 units²"

or "60 squared units"

Be careful, don't just write "60", "60 squared", or "60²". That isn't correct, technically, and some teachers will mark the answer wrong just because of that.

And there you go. Congratulations, it wasn't easy!

May God bless you.

Answer 3

In an isosceles triangle there are two equal sides. I am going to assume that the base is the unequal side. If the perimeter is 36, and we know that the base is 10, we can subtract 10 from 36 and get the combined length of the other two sides: 36 - 10 = 26 Since the other two sides are of equal length, just divide that by 2: 26 / 2 = 13 So each of the equal sides have a length of 13. To find the area of a triangle use the equation: A = (1/2)bh Where b is the base and h is the height. We know the base is 10, but we don't know the height yet. We can find it by applying the Pythagorean Theorum. If we draw a line down the center of our triangle we will get two right triangles with a base of 5 and a hypotenuse of 13. We will call the base b and the hypotenuse c and apply the Pythagorean Theorum: a^2 + b^2 = c^2 a^2 + 5^2 = 13^2 a^2 + 25 = 169 a^2 = 144 a = 12 We now know the height is 12. Going back to the area formula we can plug in our numbers: A = (1/2)(10)(12) A = 60

Answer 4

An isosceles triangle has two sides that are the same, and a base. So if the base is 10 and the perimeter is 36, you know that the length of the two remaining sides is 36 - 10 = 26. Since they are the same, you know that each side is 26/2 = 13.

Now that we know the dimensions of each side, draw an imaginary line straight down the middle of the triangle. You should now have two right triangles with a base of 5, a side of 13, and another side of x. Using the pythagorian theorem, we can deduce that x = 12.

Now the following is an easy way to compute the area of a triangle: Area = a*h/2

where a = the base and h = height.

We know the base is 10, and the imaginery line we drew down the middle, which ended up being 12, is the height, which means

Area =10*12/2

Hopefully you can take it from there =)

Answer 5

isosceles triangle means the other two sides are the same

If the perimeter is 36 and the base is 10, then we have 26 for the other sides. Split it up for 13 on each side.

base is 10 and sides are 13

Now, depends what level you are?
If you know Heron;s Formula?
A = sqrt [ 18 * (18-10)(18-13)(18-13) ]
= sqrt 3600
= 60

if you do not know Heron's then A = 1/2 base*height
we need to find height. Set up right triangles and Use pythagorean Theorem to find the height. We know the base is 5 and hyp is 13. a^2+b^2 = c^2
13^2 - 5^2 = 144 ====> height=12

A = 1/2 (10) (12) = 60

Answer 6

If the base is 10, the other two sides total 26, or 13 each. Draw a perpendicular from the apex to the base; it will divide the triangle into two right triangles with base 5 and hypotenuse 13. Pythagoras easily gives the altitude as 12, so the total area is 5 x 12 = 60.

Answer 7

Pereimter=a+2b where b is the two equal sides
36=10+2b
2b=26
b=13

So, now imagine a right triangle made from one of the 13 long sides, half the base, and the line straight down from the vertex, biseting the base. So, in the pythagoreon theorem:

a^2=b^2+c^2
(13)^2=5^2+c^2
13^2-5^2=c^2
c=sqrt(13^2-5^2)= 12

So, we have base 10 and height 12, so plugging into the equation for the area of a triangle:

a=1/2bh
a= (1/2)(10)(12)= 60

Answer 8

Well your base in 10...
And the Perimeter is 36...
The perimeter is the outside...
36=10+26
36=10+13+13<<<
a= 1/2 L H

H= the square route of b squared minus 1/4 times A squared...

Answer 9

isosceles means the other two sides excluding the base are equal. let them be equal to x.
so Perimeter=base +x+x=2x+10=36
so x=13
Area=1/2*base*height
for height we may use Pythagoras theorem. look at the half triangle made by the perpendicular bisector of the base that passes through the top vertex.
for this half triangle; hypotenuse is 13, base is 10/2=5
so height =12
Now are of the whole triangle
= 1/2 * 10 * 12
=60

Answer 10

Perimeter = the total length of the three sides of the triangle
since one side is 10 then the sum of the other two sides is 26

since the other two sides are equal, then each = 26/2=13
if you draw a perpendicular line from where the other two sides meet to the base, it will devide the base into two halves, each is 5
the height can be found by subtracting the square of 5 from the square of 13 and then it would be equal the square root of the result
H=square root of (13*13-5*5)
H=square root of 144
H=12
Area = 1/2 base * height
Area = 1/2 * 5 * 12
Area = 1/2* 60
Area = 30