Step 1: Concept. Plasmodium malariae has a characteristic morphology on the peripheral blood smear. As the parasite grows inside the red cell it stretches across the cell to form a so-called band form.
Step 2: Which stage. The band form is a growing (developing) trophozoite of P. malariae. The cytoplasm spreads as a band across the diameter of the infected red blood cell, with golden-brown malarial pigment. So option (b), the trophozoite stage, is correct.
Step 3: Why the others are wrong. The schizont stage of P. malariae shows segmentation into about 8 merozoites, often arranged as a rosette or daisy-head, not a band. A merozoite is the small invasive form released when the schizont ruptures. The gametocyte is the rounded sexual stage that fills the red cell and is taken up by the mosquito.
Step 4: Note. The band-form trophozoite is a useful clue to distinguish P. malariae from P. vivax and P. falciparum on a blood film.