Question

instructions: find the area of each figure. round to the nearest hundredth where necessary. 1. 21 m 33 m 2. 11 in 7 in 8.1 in 15 in 4. 16 cm 20.5 cm 27 cm 6. 17.6 mm 8. 44 in 10. 29.1 in 14.6 in 20.4 in

Explanation:

Step1: Recall area formulas

For a parallelogram: $A = base\times height$; for a trapezoid: $A=\frac{(a + b)h}{2}$ (where $a$ and $b$ are the lengths of the parallel - sides and $h$ is the height); for a triangle: $A=\frac{1}{2}\times base\times height$; for a square: $A = s^{2}$ (where $s$ is the side - length); for a semi - circle: $A=\frac{1}{2}\pi r^{2}$ (where $r$ is the radius).

Step2: Solve for figure 2 (trapezoid)

$a = 11$ in, $b = 15$ in, $h = 7$ in. $A=\frac{(11 + 15)\times7}{2}=\frac{26\times7}{2}=91$ in².

Step3: Solve for figure 4 (triangle)

$base = 27$ cm, $height = 16$ cm. $A=\frac{1}{2}\times27\times16=216$ cm².

Step4: Solve for figure 6 (square)

$s = 17.6$ mm. $A=(17.6)^{2}=309.76$ mm².

Step5: Solve for figure 8 (semi - circle)

$diameter = 44$ in, so $radius r = 22$ in. $A=\frac{1}{2}\pi r^{2}=\frac{1}{2}\pi\times(22)^{2}=\frac{1}{2}\pi\times484 = 242\pi\approx759.22$ in².

Step6: Solve for figure 10 (triangle)

$base = 20.4$ in, $height = 14.6$ in. $A=\frac{1}{2}\times20.4\times14.6 = 149.88$ in².

Answer:

Figure 2: 91 in²; Figure 4: 216 cm²; Figure 6: 309.76 mm²; Figure 8: 759.22 in²; Figure 10: 149.88 in²