Question

Find the surface area of the composite solid. Round the answer to the nearest hundredth

Answer 1

Total area = 135 .39 square yard

Explanation:

Given : composite figure.

To find : Find the surface area of the composite solid. Round the answer to the nearest hundredth.

Solution : We have given a composite figure with rectangle base and four triangles .

Base of two triangle = 4 yd .

Height of two triangle = √13 yd .

Base of other two triangle = 6 yd .

Height of other two triangle = 2√2 yd .

Area of rectangle = length * width .

Area of rectangle = 6 *4

Area of rectangle = 24 square yard .

Area of all rectangle = 3 *24 = 72 square yard

Area of two square = 2( 4*4) = 32 square yard.

Area of triangle =
`(1)/(2) base * height`.

Area of triangle=
`(1)/(2) 4 *√13`.

Area of triangle = 2√13 .

Area of two triangle = 2 * 2√13 .

Area of two triangle = 4√13 square yard.

Area of other triangle =
`(1)/(2) 6 * 2√2`.

Area of other triangle = 3* 2√2

Area of other triangle = 6√2.

Area of other two triangle = 2 *6√2.

Area of other two triangle = 12√2 square yard.

Total area = Area of 3 rectangle + Area of two triangle + Area of other two triangle + area of square

Total area = 72 + 4√13 + 12√2 + 32

Total area = 135 .39 square yard.

Therefore, Total area = 135 .39 square yard.

Answer 2

135.39

Explanation:

The solid consist of 4 triangles and a 5 rectangles.

Formula to calculate area of triangle is

1/2 (height) (base)

Formula to calculate area of rectangle is

length x width

so

Total surface area of the composite solid is

2( 4(4) + 6(4) + 1/2(√13)(4) + 1/2(2√2)(6) ) + 6(4)

111.39 + 24

135.39