Answer:
Area of the composite figure = 75.25 cm²
Step-by-step explanation:
Question (4). Given figure is a composite figure having,
(1). Right triangle STU
(2). A kite PSUV
(3). A trapezoid PQRS
Now we will calculate the area of each figure.
(1). Area of the right triangle = [tex]\frac{1}{2}(\text{ST})(\text{TU})[/tex]
= [tex]\frac{1}{2}(3.5)(3)[/tex]
= 5.25 cm²
(2). Area of the kite PSUV = [tex]\frac{1}{2}(\text{Diagonal 1})(\text{Diagonal 2})[/tex]
= [tex]\frac{1}{2}(\text{PU})(\text{SV})[/tex]
= [tex]\frac{1}{2}(\text{TS+RQ})(\text{SV})[/tex]
= [tex]\frac{1}{2}(3.5+7)(6)[/tex] [Since SV = 2 × 3 = 6 cm]
= [tex]3\times 10.5[/tex]
= 31.5 cm²
(3). Area of the trapezium = [tex]\frac{1}{2}(b_1+b_2)(h)[/tex] [Where [tex]b_1[/tex] and [tex]b_2[/tex] are the bases and h is the distance between the bases]
= [tex]\frac{1}{2}[(7-3)+7](7)[/tex]
= [tex]\frac{77}{2}[/tex]
= 38.5 cm²
Total area of the given figure = 5.25 + 31.5 + 38.5
= 75.25 cm²
