Given the equal legs with measurement of 16 units each, and base with length of 10 units, the altitude/height is computed using the Pythagorean theorem because the altitude perpendicular to the base divides the isosceles triangle into two congruent right triangles.
(Height)² = (16)² - (10/2)²
(Height)² = 256 - 25
[tex] \sqrt{(Height) ^{2} } = \sqrt{231} [/tex]
[tex]Height = \sqrt{231} [/tex]
Area of the triangle = (bh)/2
Area = [(10)[tex] \sqrt{231} [/tex]] ÷ 2
Area = 10√231
2
Area = 5√231
Area ≈ 5 (15.19868)
Area ≈ 75.9934
Area ≈ 76 sq. units
(Click image below to see the solution and illustration)
