Question

2. The figure shows a prism standing on a horizontal, rectangular base BCDE. ABC is a vertical cross section of the prism.

Complete the table.

3. The figure shows an empty hall. Without taking into consideration the thickness of the walls and the roof, find the air space in the hall.

Tolong bantu jawab (35 poin) ​

Answer 1

(2.)
Area of ΔABC = AB×BC÷2
Volume of prism = Area of ΔABC×CD

(part a.)
Area of ΔABC = AB×BC÷2
Area of ΔABC = 3×4÷2 = 12÷2
Area of ΔABC = 6 cm²
Volume of prism = Area of ΔABC×CD
Volume of prism = 6×7
Volume of prism = 42 cm³

(part b.)
BC = (2÷AB)×Area of ΔABC
BC = (2÷9)×63
BC = 2×7
BC = 14 cm
Volume of prism = Area of ΔABC×CD
Volume of prism = 63×11
Volume of prism = 693 cm³

(part c.)
Area of ΔABC = Volume of prism÷CD
Area of ΔABC = 72,000÷300
Area of ΔABC = 240 cm²
AB = (2÷BC)×Area of ΔABC
AB = (2÷15)×240
AB = 2×16
AB = 32 cm

(part d.)
Area of ΔABC = AB×BC÷2
Area of ΔABC = 24.6×7.8÷2 = 24.6×3.9
Area of ΔABC = 95.94 cm²
CD = Volume of prism÷Area of ΔABC
CD = 38,376÷95.94
CD = 400 cm

(3.)
Given that a prismatic hall
with the façade made out
of two trapezoids with the
--> upper base length (a) = 23 m
--> lower base length (b) = 38 m
--> base height (h) = 21 m
with the depth of the building:
--> hall depth (d) = 80 m
Find the air space
Air space =
base × depth
2×(trapezoid area) × d =
2×(a+b)×(h/2) × d =
(a+b)× h × d
(23+38)×21×80 =
61×1,680 =
102,480 m³ of air space

( x c v i )