Final answer:
To find the area of an isosceles triangle with given side lengths, we draw an altitude to form two right triangles, use the Pythagorean theorem to find the height, and then use the formula for the area of a triangle (Area = 1/2 × base × height). The area of the isosceles triangle is approximately 112.2 mm2 rounded to the nearest tenth.
Step-by-step explanation:
To find the area of an isosceles triangle with sides of length 23 mm, 23 mm, and a base of 10 mm, we need to use the fact that an isosceles triangle has two sides of equal length and the angles opposite those sides are also equal. First, we can split the triangle into two right triangles by drawing an altitude from the apex opposite the base to the midpoint of the base. This altitude will be the height of the triangle that we need to calculate its area.
To find the height (h) of the triangle, we can apply the Pythagorean theorem to one of the right triangles formed. The hypotenuse is one of the equal sides of the isosceles triangle (23 mm), and half of the base (b/2) is 5 mm. This gives us:
h = √(232 - 52) = √(529 - 25) = √504
We then use the area formula for a triangle: Area = 1/2 × base × height.
Therefore, Area = 1/2 × 10 mm × √504 mm which simplifies to 5 × √504 mm2. Finally, to find the area in square millimeters, and round to the nearest tenth, Area ≈ 5 × 22.44994 mm2 ≈ 112.2 mm2