Question

1
numeric 1 point
find the total surface area of the figure. 15
answer

Explanation:

Step1: Calculate area of right triangle

The right triangle has legs 8 and 15. Area formula: $\frac{1}{2} \times base \times height$
$\frac{1}{2} \times 8 \times 15 = 60$

Step2: Find base of the triangle

First, find the hypotenuse of the right triangle (shared side) using Pythagoras: $c = \sqrt{a^2 + b^2}$
$\sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17$

Step3: Calculate area of isosceles triangle

The isosceles triangle has sides 17, 18, 18. Use Heron's formula: $s = \frac{17+18+18}{2} = 26.5$, area $= \sqrt{s(s-a)(s-b)(s-c)}$
$\sqrt{26.5 \times (26.5-17) \times (26.5-18) \times (26.5-18)} = \sqrt{26.5 \times 9.5 \times 8.5 \times 8.5} = \sqrt{26.5 \times 9.5 \times 72.25} = \sqrt{18194.4375} = 134.89$

Step4: Sum the two areas

Total surface area = area of right triangle + area of isosceles triangle
$60 + 134.89 = 194.89$

Answer:

194.89