Question

determine the base of the triangle. area: 52 ft² height: 8 ft; determine the height of the triangle. area: 102 cm² base: 8.5 cm; determine the area of the parallelogram. base: 12 yd height: 15 yd; determine the area of the parallelogram. base: 7 mm height: 7.5 mm; determine the area of the trapezoid. base 1: 6.5 cm base 2: 3.5 cm height: 5.8 cm; determine the area of the trapezoid. base 1: 18.4 cm base 2: 10 cm height: 12.5 cm

Explanation:

Step1: Recall triangle - base formula

The area formula for a triangle is $A=\frac{1}{2}bh$, where $A$ is the area, $b$ is the base, and $h$ is the height. For the first triangle with $A = 52$ ft² and $h=8$ ft, we can solve for $b$: $b=\frac{2A}{h}$.
$b=\frac{2\times52}{8}=13$ ft.

Step2: Recall triangle - height formula

For the second triangle with $A = 102$ cm² and $b = 8.5$ cm, using $A=\frac{1}{2}bh$, we solve for $h$: $h=\frac{2A}{b}$.
$h=\frac{2\times102}{8.5}=24$ cm.

Step3: Recall parallelogram - area formula

The area formula for a parallelogram is $A = bh$. For the first parallelogram with $b = 12$ yd and $h = 15$ yd, $A=12\times15 = 180$ yd².

Step4: Recall parallelogram - area formula

For the second parallelogram with $b = 7$ mm and $h = 7.5$ mm, $A=7\times7.5=52.5$ mm².

Step5: Recall trapezoid - area formula

The area formula for a trapezoid is $A=\frac{(b_1 + b_2)h}{2}$. For the first trapezoid with $b_1=6.5$ cm, $b_2 = 3.5$ cm and $h = 5.8$ cm, $A=\frac{(6.5 + 3.5)\times5.8}{2}=\frac{10\times5.8}{2}=29$ cm².

Step6: Recall trapezoid - area formula

For the second trapezoid with $b_1 = 18.4$ cm, $b_2=10$ cm and $h = 12.5$ cm, $A=\frac{(18.4 + 10)\times12.5}{2}=\frac{28.4\times12.5}{2}=177.5$ cm².

Answer:

1. Triangle base: 13 ft
2. Triangle height: 24 cm
3. Parallelogram area 1: 180 yd²
4. Parallelogram area 2: 52.5 mm²
5. Trapezoid area 1: 29 cm²
6. Trapezoid area 2: 177.5 cm²