Question

i. find the perimeter and the area of each parallelogram.①5 in.4 in.8 in.②16 m12 m5 m③3.6 cm3.2 cm5.1 cm④90 ft90 ft100 ft⑤6.5 cm4.2 cm9.3 cm⑥2.0 m0.7 m1.8 mii. solve.⑦ the base of a parallelogram is 10 in.the height is 2 in. more than half thebase. find the area.⑧ the height of a parallelogram is 4.5 cm.the base is twice the height. what isthe area?⑨ the area of a parallelogram is 60 ft².the height is 5 ft. how long is thebase?⑩ the area of a parallelogram is 375 cm².the base is 25 cm. find the height.| t | sh | he | re | e | we | wa | it || ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- || 31.6 cm | 17.4 cm | 33.8 cm | 15 cm | 32 in.² | 56 m | 1.38 m² | 70 in.² || sc | a | nt | en | da | re | al | t || 37.6 cm² | 180 m² | 12 ft | 18 m | 380 ft | 1.26 m² | 16.32 cm² | 16 ft || pr | im | v | et | ty | is | er | it || 5.4 m | 350 ft | 39.06 cm² | 84 in.² | 40.5 cm² | 28 in. | 6.3 m | 8,100 ft² |

Explanation:

Part I: Figures ①-⑥

The formula for the perimeter of a parallelogram is $P = 2(a + b)$, where $a$ and $b$ are the lengths of adjacent sides.
The formula for the area of a parallelogram is $A = b \times h$, where $b$ is the base and $h$ is the corresponding height.

Figure ①

Step1: Calculate perimeter

$P = 2(5 + 8) = 2(13) = 26$ in

Step2: Calculate area

$A = 8 \times 4 = 32$ in²

Figure ②

Step1: Calculate perimeter

$P = 2(16 + 12) = 2(28) = 56$ m

Step2: Calculate area

$A = 12 \times 15 = 180$ m²

Figure ③

Step1: Calculate perimeter

$P = 2(3.6 + 5.1) = 2(8.7) = 17.4$ cm

Step2: Calculate area

$A = 5.1 \times 3.2 = 16.32$ cm²

Figure ④

Step1: Calculate perimeter

$P = 2(90 + 100) = 2(190) = 380$ ft

Step2: Calculate area

$A = 90 \times 90 = 8100$ ft²

Figure ⑤

Step1: Calculate perimeter

$P = 2(6.5 + 9.3) = 2(15.8) = 31.6$ cm

Step2: Calculate area

$A = 9.3 \times 4.2 = 39.06$ cm²

Figure ⑥

Step1: Calculate perimeter

$P = 2(2.0 + 0.7) = 2(2.7) = 5.4$ m

Step2: Calculate area

$A = 0.7 \times 1.8 = 1.26$ m²

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Part II: Problems ⑦-⑩

Problem ⑦

Step1: Define height variable

Let base $b = 10$ in, height $h = \frac{1}{2}(10) + 2 = 7$ in

Step2: Calculate area

$A = 10 \times 7 = 70$ in²

Problem ⑧

Step1: Define base variable

Let height $h = 4.5$ cm, base $b = 2(4.5) = 9$ cm

Step2: Calculate area

$A = 9 \times 4.5 = 40.5$ cm²

Problem ⑨

Step1: Rearrange area formula for base

$b = \frac{A}{h}$, where $A=60$ ft², $h=5$ ft

Step2: Solve for base

$b = \frac{60}{5} = 12$ ft

Problem ⑩

Step1: Rearrange area formula for height

$h = \frac{A}{b}$, where $A=375$ cm², $b=25$ cm

Step2: Solve for height

$h = \frac{375}{25} = 15$ cm

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Answer:

Part I (Perimeter | Area)

1. 26 in | 32 in²
2. 56 m | 180 m²
3. 17.4 cm | 16.32 cm²
4. 380 ft | 8100 ft²
5. 31.6 cm | 39.06 cm²
6. 5.4 m | 1.26 m²

Part II

1. 70 in²
2. 40.5 cm²
3. 12 ft
4. 15 cm

Table Completion (Matching values to labels):

T: 31.6 cm, SH:17.4 cm, HE:33.8 cm, RE:15 cm, E:32 in², WE:56 m, WA:1.38 m², IT:70 in²
SC:37.6 cm², A:180 m², NT:12 ft, EN:16 m, DA:380 ft, RE:1.26 m², AL:16.32 cm², T:16 ft
PR:5.4 m, IM:380 ft, V:39.06 cm², ET:84 in², TY:40.5 cm², IS:28 in, ER:6.3 m, IT:8100 ft²