1. The base of a right prism is a triangle whose sides arc of lengths 13 cm., 20 cm. and 21 cm. If the height of the prism be 9 cm. find the area of total lateral surface, area of the whole surface and the volume of the prism.
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Solution:
Let s be the semi-perimeter of the triangular base of the prism. Then, S = (13 + 20 + 21)/2 cm. = 27 cm.
Therefore, the area of the prism = √[s(s - a)(s - b)(s - c)]
= √(27(27 - 13)(27 - 20)(27 - 21)) sq. cm.
= √(27 × 14 × 7 × 6) sq. cm.
= 9 × 7 × 2 sq. cm.
Therefore, the area of total lateral surface of the prism
= (perimeter of the base) × height
= (486 + 2 × 126) sq. cm.
And the volume of the prism
= area of the base × height
= 126 × 9 cu.cm.
= 1134 cu.cm.
⚘ ᴄʜᴇꜱᴋᴀ ⚘
“ɴᴇᴠᴇʀ ꜱᴛᴏᴘꜱ ʟᴇᴀʀɴɪɴɢ, ʙᴇᴄᴀᴜꜱᴇ ʟɪꜰᴇ ɴᴇᴠᴇʀ ꜱᴛᴏᴘꜱ ᴛᴇᴀᴄʜɪɴɢ”
Solution:
Let s be the semi-perimeter of the triangular base of the prism. Then, S = (13 + 20 + 21)/2 cm. = 27 cm.
Therefore, the area of the prism = √[s(s - a)(s - b)(s - c)]
= √(27(27 - 13)(27 - 20)(27 - 21)) sq. cm.
= √(27 × 14 × 7 × 6) sq. cm.
= 9 × 7 × 2 sq. cm.
Therefore, the area of total lateral surface of the prism
= (perimeter of the base) × height
= (486 + 2 × 126) sq. cm.
And the volume of the prism
= area of the base × height
= 126 × 9 cu.cm.
= 1134 cu.cm.
⚘ ᴄʜᴇꜱᴋᴀ ⚘
“ɴᴇᴠᴇʀ ꜱᴛᴏᴘꜱ ʟᴇᴀʀɴɪɴɢ, ʙᴇᴄᴀᴜꜱᴇ ʟɪꜰᴇ ɴᴇᴠᴇʀ ꜱᴛᴏᴘꜱ ᴛᴇᴀᴄʜɪɴɢ”