Notes on Triangular prism | Grade 10 > Compulsory Mathematics > Mensuration | KULLABS.COM

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• Quiz #### Volume and surface area of Triangular prism

A prism with the triangle as the base is called triangular prism. In the case of a triangular prism, two congruent and parallel triangles ABC and EFG are called the base of the prism. Area of each triangle is called base area or area of the base.

The lateral faces (AEFB, AEGC and BCGF), are rectangles formed by joining corresponding vertices of the bases. The intersection of lateral faces is lateral edges.

The length or height  ( AE, BF, CG ) is the perpendicular distance between the bases. The lateral surface is the total area of the lateral faces (The length times the perimeter of base) and volume is equal to the product of base area and its length or height.

So,

Area of triangular base = Area of  ΔABC or Area of ΔEFG

Lateral (Curved) Surface Area (L.S.A) = Perimeter of triangular base × length

Total Surface Area (T.S.A) = 2 × Area of triangular base + L.S.A.

Volume of triangular prism = Area of triangular base × length (or height of prism)

Area of triangular base = Area of  ΔABC or Area of ΔEFG

Lateral (Curved) Surface Area (L.S.A) = Perimeter of triangular base × length

Total Surface Area (T.S.A) = 2 × Area of triangular base + L.S.A.

Volume of triangular prism = Area of triangular base × length (or height of prism)

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#### Click on the questions below to reveal the answers

Solution:

Here,

\begin{align*}\text{base area of prism (A)} &= \frac{1}{2} \times base \times height \\ &= \frac{1}{2} \times 6 \times 8 \\ &= 24 \: cm^2 \end{align*}

height of prism (h) = 30 cm
By formula,

$$Volume\: of \: prism (V) = A\times h = 24 \times 30 = 720\:cm^2 \: \: _{Ans}$$

Solution:

BC = B'C' = 5 cm

\begin{align*} \text{Perimeter of the base triangle} &= AB+BC+AC\\ &= 3cm+5cm+AC \\ &= 8cm+AC \\ Height \: of\: the \: prism (h) &= 20\: cm \\ Rectangular \: surface \: area \: of\:prism &=ph \\ or, 240cm^2 &= (8cm + AC) .20cm \\ or, 8cm + AC &= \frac{240cm^2}{20cm}\\ or, 8cm+AC &= 12cm \\ or, AC &= 12cm-8cm \\ \therefore AC &= 4 cm \: _{Ans}\end{align*}

Solution:

\begin{align*} 2s &= PQ+PR+QR \\or, 2s &= (6+7+5)cm \\or,2s &= 18 cm \\ or, s&=\frac{18}{2}\\ \therefore s &= 9cm \end{align*}

Now,

\begin{align*} Area \: of \: \Delta PQR &= \sqrt{s(s-a)(s-b)(s-c)}\\ &= \sqrt{9 (9-6)(9-7)(9-5)}cm^2\\ &= \sqrt{9\times3\times2\times4}cm^2 \\ &= \sqrt{216}cm^2 \\ \: \\ Volume \: of \: prism &= A \times height \\ &= \sqrt{216}\times18 \: cm^3 \\ &= 264.54 \: cm^3 \end{align*}

Solution:

Here, AE =10cm, AF = BC = 8cm

$$EF = \sqrt{AE^2 - AF^2 } = \sqrt{10^2 - 8^2} = \sqrt{36} = 6 cm$$

$$\text{Perimeter of base triangle} = 10cm + 8cm+6cm = 24 cm$$

height (h)= 20cm

\begin{align*} \text{Lateral surface area } \: &= P \times h \\ &= 24 cm \times 20 cm \\ &= 480 cm^2 \: \: \: _{Ans}\end{align*}

Solution:

Here,

$$P = AB + BC + CA \\ \: \: \: = 2\sqrt{3} + 2\sqrt{3} + 2\sqrt{3}\\ \: \: \: = 6\sqrt{3} cm$$

\begin{align*} \text{Area of rectangular surface}&= P \times CK \\ &= 6\sqrt{3}\times 4\sqrt{3}\\ &= 72cm^2 \: _{Ans} \end{align*}

Solution:

\begin{align*} The \:area (A) \: of \: the \: base &= l^2\\ &= (6cm)^2 \\&=36cm^2 \\ Perimeter (P)\: of \: of \: the \: base &= 4l \\ &=4 \times 6 \\ &=24cm \\ The \: height(h) of \: the\:prism&=12 \\ Here, \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ Total\:surface\:area &= 2 \times area \: of \: base + L.S.A \\ &= 2A + Ph\\ &= 2\times36+24\times12 \\ &= 72cm^2+288cm^2 \\ &= 360cm^2 \end{align*}

Solution:

Let h be the height of the prism.
Here, Volume = 48cm3

Area of base triangle (A) =?

\begin{align*} A &= \frac{1}{2} \times 4 \times 3 \\ &= 6 \: cm^2 \\ By \: formula, \\ Volume &= A \times h \\48^3 &= 6cm^2 \times h \\ or, h &= \frac{48cm^3}{6cm^2} \\ \therefore h &= 8 cm \: \: _{Ans} \end{align*}

Solution:

Length of the side of the base (a) = 6 cm

\begin{align*}Area \: of \: base\: triangle\: (A)&= \frac{\sqrt{3}}{4}a^2 \\ &= \frac{\sqrt{3}}{4}6^2 \\ &= 9\sqrt{3} \: cm^2 \\ Volume(V) &= 162 \: cm^3\\ height \: of \: the \: prism \: (h)&= ? \\ We \: know \: that, \: \: \:\:\:\:\:\:\:\:\:\: \\ V&=A \times h \\ 162 \:cm^3&=9\sqrt{3} \times h \\ or, h &= \frac{162}{9\sqrt{3}} \\ or, h &= 6\sqrt{3} \\ \therefore h &= 10.39 \: cm \end{align*}

Solution:

\begin{align*} Perimeter \: of \: base \: triangle \: (P) &= AB+BC+AC \\ &= 3cm+5cm+4cm\\&= 12cm\\ Height \: (h) \:\:= CC' &= ? \\ By, formula, area \: of \: rectangular \: faces &= Ph \\ or, 240 \: cm^2 &= 12cm\times h \\ or,h&=\frac{240cm^2}{12cm}\\ \therefore h &= 20cm \: _{Ans} \end{align*}

Solution:

Perimeter of base (P) = ?
Rectangular surface area (S) = 600 cm2
Height of prism (h) = 32 cm
By formula,

\begin{align*} S &=Ph \\ or, 660&=P\times 22 \\ or, P &= \frac{660}{22}\\ \therefore P &= 30 \: cm \: _{Ans} \end{align*}

Solution:

Here,

\begin{align*} BC &= \sqrt{AC^2-AB^2}\\ &=\sqrt{(20cm)^2 - (12cm)^2}\\ &=\sqrt{400-144}cm \\ &= \sqrt{256}cm \\ &= 16cm \\ \: \\ \text{Area of right angled} \: &triangle \: of \: base \: (A) = \frac{1}{2}\times AB \times BC \\ &= \frac{1}{2} \times 12 \times 16 \\ &= 6cm \times 16cm \\ &= 96cm^2 \\ \: \\ Suppose, height \: of \: the \: prism &= h \\ Then, volume \: of \: the \: prism &= Ah \\ or, 1920cm^3 &= 96cm^2\times h \\ or, h &= \frac{1920cm^3}{96cm^2}\\ \therefore h &= 20 cm \: _{Ans} \: cm \end{align*}

0%

750 cm3

720 cm2

721 cm3

700 cm3

25 cm

23 cm

22 cm

24 cm

615 cm3

620 cm3

630 cm3

600 cm3

420 cm3

436 cm3

450 cm3

430 cm3

14 cm

10 cm

9 cm

8 cm

8 cm

10 cm

6 cm

4 cm

• ### The area and perimeter of base of a prism are 30 cm2  and 25 cm respectively. If the total surface  area of the prism is 360 cm2, find the height and lateral surface area of the prism.

15 cm, 200cm2

12 cm, 300 cm2

13 cm, 150 cm2

10 cm, 100 cm2

• ### The  area of rectangular faces of a triangular prism is 432 cm2,, height 18  cm and  the ratio  of base  of sides is 3: 4: 5. Find  the base sides of the prism.

7 cm,8 cm,9 cm

6 cm, 8 cm, 10 cm

4 cm, 5 cm, 9 cm

5 cm, 6 cm, 8 cm

50 cm, 34 cm

40 cm,24 cm

20 cm, 22 cm

30 cm,33 cm

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