# Question #048ff

Feb 22, 2018

Hence, theWhole surface area is

$124 + 550 + 124 = 798 c {m}^{2}$

Volume = Area of the base x height

$V = 124 \times 12.5 = 1550 c {m}^{3}$

#### Explanation:

1)
The base can be considered a a combination of
A square of side 10 cm
A triangle with base as 6 cm and altitude as 8 cm.
$\sqrt{{6}^{2} + {8}^{2}} = 10$
Thus, the area of the top face = area of bottom face =
$\text{Area of square " + "Area of "right angle triangle}$
$A r e a o f \square = 10 \times 10 = 100 c {m}^{2}$
$\text{Area of } r i g h t \angle \triangle = \frac{1}{2} \times 6 \times 8 = \frac{1}{2} \times 48 = 24$

Area of top face $= 100 + 24 = 124 c {m}^{2}$

Area of bottom face $= 100 + 24 = 124 c {m}^{2}$

Perimeter = 10+10+10+6+8=30+14=44cm

$H e i g h t = 12.5 c m$

Area of the lateral surface=Perimeter x Height

Area of the lateral surface$= 44 \times 12.5 = 550 c {m}^{2}$

Hence, the total area is

$124 + 550 + 124 = 798 c {m}^{2}$

Volume = Area of the base x height

$V = 124 \times 12.5 = 1550 c {m}^{3}$