Question

emaan designs the birdhouse shown to the right.
a. what is the total height of the birdhouse? show your work.
b. if emaan decides to change the design by increasing each side of the roof from 12.5 cm to 15.2 cm, what will be the new height of
c. height of the top part = (12.5)² - (9.2)²
d. height of the top part = √(12.5)² - (9.2)²
the total height of the birdhouse is
(type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Calculate roof height

The roof is an isosceles triangle. The slant side is \(12.5\) cm, half the base is \(9.2\) cm. Using Pythagoras: \(h_{roof}=\sqrt{(12.5)^2 - (9.2)^2}\).

$$h_{roof}=\sqrt{156.25 - 84.64}=\sqrt{71.61}=8.46$$

(approx)

Step2: Total height

The lower part height is \(9.2\) cm. Total height \(= h_{roof}+9.2\).

$$8.46 + 9.2 = 17.66\approx17.7$$

(rounded to nearest tenth)

Answer:

\(17.7\)