This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Haya Icekid, tuendelee na maswali yaliyobaki. Swali la 1: Kokotoa eneo la sehemu isiyo na kivuli katika mchoro hapa chini. Mchoro unaonyesha mstatili mkubwa wenye mstatili mdogo wenye kivuli ndani yake. Urefu wa mstatili mkubwa ni 36 cm na upana ni 25 cm. Urefu wa mstatili wenye kivuli ni 20 cm na upana ni 18 cm. Step 1: Pata eneo la mstatili mkubwa. A_mkubwa = urefu × upana = 36 cm × 25 cm A_mkubwa = 900 cm^2 Step 2: Pata eneo la mstatili wenye kivuli. A_kivuli = urefu × upana = 20 cm × 18 cm A_kivuli = 360 cm^2 Step 3: Kokotoa eneo lisilo na kivuli. Eneo lisilo na kivuli = Eneo la mstatili mkubwa - Eneo la mstatili wenye kivuli A_isiyo\_kivuli = 900 cm^2 - 360 cm^2 Eneo lisilo na kivuli = 540 cm^2 Swali la 2b: Kokotoa eneo lililotiwa kivuli katika mchoro hapa chini. Mchoro unaonyesha mraba wenye nusu duara ndani yake. Sehemu iliyotiwa kivuli ni ile iliyo ndani ya mraba lakini nje ya nusu duara. Kutokana na gridi, tunaweza kudhani upande wa mraba ni 4 cm. Kipenyo cha nusu duara ni sawa na upande wa mraba, hivyo kipenyo ni 4 cm. Rediasi ya nusu duara ni r = (4)/(2) = 2 cm. Step 1: Pata eneo la mraba. A_mraba = upande^2 = (4 cm)^2 A_mraba = 16 cm^2 Step 2: Pata eneo la nusu duara. (Tumia = (22)/(7)) A_nusu\_duara = (1)/(2) r^2 = (1)/(2) × (22)/(7) × (2 cm)^2 A_nusu\_duara = (1)/(2) × (22)/(7) × 4 cm^2 A_nusu\_duara = (44)/(7) cm^2 ≈ 6.2857 cm^2 Step 3: Kokotoa eneo lililotiwa kivuli. Eneo lililotiwa kivuli = Eneo la mraba - Eneo la nusu duara A_kivuli = 16 cm^2 - (44)/(7) cm^2 A_kivuli = (16 × 7 - 44)/(7) cm^2 = (112 - 44)/(7) cm^2 A_kivuli = (68)/(7) cm^2 Eneo lililotiwa kivuli = 9.71 cm^2 (kwa sehemu mbili za desimali) That's 2 down. 3 left today — send the next one.