What is the surface area of this figure? Enter your answer in the box. ft² Complex solid composed of a triangular prism and a rectangular prism. The triangular prism is centered on the top of the rectangular prism. The rectangular prism bottom face is labeled 15 ft and 5 ft. The height of the rectangular prism is labeled 8 ft. The triangular base has an altitude drawn and labeled 7 ft. The sides of the triangle are labeled 9 ft, 9 ft, and 11 ft. The height of the triangular prism is 5 ft.

Answer:

a = side length a

b = side length b = bottom triangle base b

c = side length c

h = height of prism

H = height of bottom triangle

V = volume

Atot = total surface area = all sides

Alat = lateral surface area = all rectangular sides

Atop = top surface area = top triangle

Abot = bottom surface area = bottom triangle

A triangular prism is a geometric solid shape with a triangle as its base. It's a three-sided prism where the base and top are equal triangles and the remaining 3 sides are rectangles.

Calculator Use

This calculator finds the volume, surface area and height of a triangular prism. Surface area calculations include top, bottom, lateral sides and total surface area. Height is calculated from known volume or lateral surface area.

Units: Units are shown for convenience but do not affect calculations. Answers will be the same whether in feet, ft2, ft3, or meters, m2, m3, or any other unit measure.

Significant Figures: Choose the number of significant figures or leave on auto to let the calculator determine number precision.

Triangular Prism Formulas in terms of height and triangle side lengths a, b and c:

Volume of a Triangular Prism Formula

Finds the 3-dimensional space occupied by a triangular prism.

V=14h(c+a−b)(a+b−c)−−−−−−−−−−−−−−−−−√×(a+b+c)(b+c−a)−−−−−−−−−−−−−−−−−√

Top Surface Area of a Triangular Prism Formula

Finds the area contained by the triangular surface at the top of the prism. This is the same area as the bottom surface area.

Atop=14(a+b+c)(b+c−a)×(c+a−b)(a+b−c)−−−−−−−−−−−−−−−−−−−−−−−√

Bottom Surface Area of a Triangular Prism Formula

Finds the area contained by the triangular surface at the bottom of the prism. This is the same area as the top surface area.

Abot=14(a+b+c)(b+c−a)×(c+a−b)(a+b−c)−−−−−−−−−−−−−−−−−−−−−−−√

Lateral Surface Area of a Triangular Prism Formula

Finds the total area contained by the three rectangular sides of the prism. You can think of the lateral surface area as the total surface area of the prism minus the two triangular areas at the top and bottom of the prism.

Alat=h(a+b+c)

Total Surface Area of a Triangular Prism Formula

Finds the total area of all sides of a triangular prism. Total surface area of a prism includes the area of the top and bottom triangle sides of the prism, plus the area of all 3 rectangular sides.

Atot=Atop+Abot+Alat

Step-by-step explanation:

Height of a Triangular Prism Formula in Terms of Volume

Finds the height of a triangular prism by solving the Volume Formula for height. Height, h, is calculated from volume, V, and side lengths a, b and c.

h=4V÷[(c+a−b)(a+b−c)−−−−−−−−−−−−−−−−−√×(a+b+c)(b+c−a)−−−−−−−−−−−−−−−−−√]

Height of a Triangular Prism Formula in Terms of Lateral Surface Area

Finds the height of a triangular prism by solving the Lateral Surface Area Formula for height. Height, h, is calculated from lateral surface area, Alat, and side lengths a, b and c.

h=Alat(a+b+c)

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The surface area of this figure will be 540 square feet.

Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.

A complex solid made out of triangular and rectangular prisms. The triangular prism is centered on the rectangular prism's top.

The surface area of the shape is given as,

SA = 2(15 x 8 + 8 x 5) + 15 x 5 + 11 x 5 + 9 x 5 + 9 x 5

SA = 2(120 + 40) + 75 + 55 + 45 + 45

SA = 2 x 160 + 220

SA = 320 + 220

SA = 540 square feet

The surface area of this figure will be 540 square feet.

More about the area link is given below.

https://brainly.com/question/27683633

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