The base of an isosceles triangle is 30 m, and the height drawn from the top of the base is 24 m.
The base of an isosceles triangle is 30 m, and the height drawn from the top of the base is 24 m. Find the area of the triangle.
1. Vertices of the triangle A, B, C. AC = 30 m. BK = 24 m.
2. Let’s draw the height of the HВ to the base of the speaker. In an isosceles triangle, she performs another
functions of the median. That is, it divides the base of the AC into two segments of the same length: AH = CH = AC / 2 = 30/2 = 15 m.
3. Triangles ABH and ACK are similar in two equal angles:
∠АНB = ∠АКС = 90 °.
∠А = ∠С as angles at the base of an isosceles triangle.
4. From the similarity of the above triangles it follows:
BН / AK = AН / СK.
5. We calculate the length of the segment of the CК using the Pythagorean theorem:
СK = √AC² – AK² = √30² – 24² = √900 – 576 = 18 m.
6. ВН / 24 = 15/18.
BH = 24 x 15/18 = 20 m.
7. Calculate the area (S) of the triangle ABC:
S = АС х ВН / 2 = 30 х 20/2 = 300 m².
Answer: the area of a given triangle is 300 m².