perimeter and area of plane figures .?

one of the equal sides of an isosceles triangle is 13 cm and its perimeter is 50 cm . find the area of thr triangle

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  • 1 decade ago
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    Okay, so in this problem, you know that two of the sides are 13 cm, because an isosceles triangle has two equal sides, and they tell you that one is 13 cm.

    So the perimeter is 13cm + 13cm + x = 50cm, where x is the length of the other side. Solve for x:

    26 cm + x = 50 cm

    x = 50cm - 26 cm = 24 cm

    So, if we look at the triangle with the two equal 13cm sides on the left and right, while the 24 cm side is at the bottom, then we can find the area with the formula for area of a triangle:

    Area of triangle = (1/2)Base * Height

    The way we have the triangle set up, the base is 24 cm. To find the height, we'll have to use some geometry.

    If we split the triangle in half vertically down the middle, we're left with two right triangles with hypotenuse 13cm and the base is (24/2).

    To find the height we can use Pythagorean Theorem which is:

    A² + B² = C²

    Where C is the hypotenuse of a right triangle, and A and B are the sides.

    We know C = 13, and we know one of the sides is (24/2)

    Plug these values in and solve for the other leg, which is the height of our Isosceles triangle.

    13² = 12² + B²

    13² - 12² = B²

    B = √ (13² - 12²)

    B = 5 cm

    Now plug them all into the area formula:

    A = (1/2)Base * Height

    (1/2)*24cm * 5cm = 120 cm²

    Hope this helps!

  • 1 decade ago

    The third side can be given as, c = 50 - (13 + 13) = 24 cm.

    Now, let's draw a line from the intersection of the two equal sides toward the third side.

    We know the property of isosceles triangles that, a line drawn from the intersection of the equal sides makes a perpendicular with the base (the third side) and bisects it.

    Now, the original triangle gets divided into two equal (or congruent) right triangles, each having base of 12 cm.

    Let's calculate the height of rt. triangles using Pythagoras Theorem.

    Height = root (13^2 - 12^2)

    = root (169 - 144)

    = root (25)

    = 5 cm.

    Therefore, the area can be given as, A = 2 * (Area of one right triangle)

    => A = 2 * (1/2) * b * h

    => A = 2 * (1/2) * 12 * 5

    => A = 60 cm x cm

    Therefore the area is, A = 60 square cm.

  • 1 decade ago

    say perimeter is sum of all sides

    as triangle is isosceles of side 13 and perimeter 50 so base is 50-26 = 24 cm

    now area if all sides are give is sqrt(s(s-a)(s-b)(s-c) where s =(1/2)(perimeter) and a, b c are sides

    so s = 1/2 50 =25 and a = 13, b =13 abd c = 24

    so area = sqrt (25 X 12 X12X 1)

    = 5 X 12 = 60 cm Square

  • 1 decade ago

    ok, so first of all, you need to figure out the other two sides. the perimeter is 50 and an isoceles triangle has 2 equal sides. so let's do 13+13=26...so, the other side is 50-26=24. the formula for the area of a triangle is Base multiplied by Height Divided by Two or in half. (BxH/2) so now the base in this case is 24x13=312. divide that by 2 and you get: 156. that's the area: 156 centimeters2/ 156 centimeters squared.

    Step 1: figuring out the 3 sides

    13,13,(50-26),24

    Step 2: Applying it to the formula--Base x Height / 2

    since there are two 13 cm's, they can't be the base. so the base is 24. so, 24*13=312

    Step 3: Divide it by 2!

    312/2=156

    Step 4: Label it!

    156 centimeters squared.

    Math Chew did a great job, seems like he is a great math person! (which i wish i could be, hehehaha!) so, i've explained it in a way that they teach us here in the US. good luck!! I hope i helped...by the way, geometry has never been my favorite subject either...haha...

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  • 1 decade ago

    you have 3 sides- a=13,b=13,c=24

    now apply HERO'S formula-

    area=sqrt[s(s-a)(s-b)(s-c)]

    s=perimeter/2 =50/2 =25cm

    area = sqrt[25*12*12*1]

    =sqrt[144*25]

    =12*5

    =60cm^2

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