Question

They have a rectangle ABCD as shown below, where AB = 24cm BC = 10cm and AE = 13cm

A. Calculate the volume of the rectangle ABCD
B. Calculate the circumference of the BCD triangle
C. Calculate the circumference of the BEC triangle
D. Calculate the circumference of the DEC triangle

Answer 1

A. Area of ABCD = 240
`cm^(2)`

B. 60 cm

C. 36 cm

D. 50 cm

Explanation:

Given: AB = 24cm BC = 10cm and AE = 13cm.

A. Since a rectangle is a 2 dimensional figure, it has no volume but area.

So that,

the area of the rectangle ABCD = length x width

= 24 x 10

= 240
`cm^(2)`

B. To calculate the circumference of the BCD triangle, apply the Pythagoras theorem to determine BD.

`BD^(2)` =
`BC^(2)` +
`DC^(2)`

=
`10^(2)` +
`24^(2)`

= 676

BD =
`√(676)`

= 26

BD = 26 cm

so that,

the circumference of BCD = 10 + 24 + 26

= 60 cm

C. To calculate the circumference of the BEC triangle,

AC = 26 cm, AE = 13 cm

CE = 26 - 13

= 13 cm

CE = 13 cm

The circumference of the BEC triangle = 13 + 13 + 10

= 36 cm

D. The circumference of the DEC triangle = 13 + 13 + 24

= 50 cm