Question

Area and volume help?

Answer 1

Area `A=42`

Explanation:

In the figure, we can split the given closed polygon into rectangles and triangles

Triangles are 4 in number

`b_1=3, h_1=2, T_1=1/2(b_1h_1)=1/2(3)(2)=3`
`b_2=4, h_2=2, T_2=1/2(b_2h_2)=1/2(4)(2)=4`
`b_3=3, h_3=2, T_1=1/2(b_1h_1)=1/2(3)(2)=3`
`b_4=4, h_4=2, T_1=1/2(b_1h_1)=1/2(4)(2)=4`

Total area of triangles `T=T_1+T_2+T_3+T_4`
`T=3+4+3+4=14`

Rectangle is 1 in number

`b=7, h=4, R=b_1h_1=(7)(4)=28`

Total area `A=T+R=14+28=42`

Area `A=42`

Answer 2

`"area "=42" square units"`

Explanation:

`"we can split the figure into 'regular' figures"`

`"the central region is a "color(blue)"rectangle"`

`"the regions above and below the rectangle are "color(blue)"triangles"`

`• " area of rectangle "="length "xx" breadth"`

`• " area of triangle "=1/2xx" base "xx" height"`

`"area of rectangle "=7xx4=28`

`"area of 2 congruent triangles "=2xx1/2xx7xx2=14`

`"area of figure "=28+14=42" square units"`