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Surface Area of Pyramid: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Surface Area of PyramidSurface Area of Pyramid: Definition and ExamplesTable of ContentsSurface Area of a Pyramid Definition of Surface Area of a Pyramid

A pyramid is a three-dimensional shape with a polygon base and triangular faces that meet at a point called the apex. The surface area of a pyramid is the sum of the areas of all its faces, including the base and all triangular lateral faces. Surface area is measured in square units such as cm², m², or in².

There are different types of pyramids named after their base shape. The most common are triangular pyramids (with a triangular base) and square pyramids (with a square base). For a regular pyramid, the surface area can be calculated using the formula: Base Area + 12\frac{1}{2}21​Ps, where P represents the perimeter of the base and s represents the slant height. The slant height is the height of a triangular face measured from the apex to the middle of a base edge.

Examples of Surface Area of a Pyramid Example 1: Finding the Surface Area of a Square Pyramid Problem:

A square pyramid has base dimensions of 75 ft×75 ft75 \text{ ft} \times 75 \text{ ft}75 ft×75 ft and its slant height is around 500 ft500 \text{ ft}500 ft. Calculate its surface area.

Step-by-step solution:

Step 1, Find the area of the base. For a square base, multiply the side length by itself.

Base Area=75×75=5625 square feet\text{Base Area} = 75 \times 75 = 5625 \text{ square feet}Base Area=75×75=5625 square feet

Step 2, Identify the slant height of the pyramid.

Slant height=50 ft\text{Slant height} = 50 \text{ ft}Slant height=50 ft

Step 3, Apply the surface area formula for a square pyramid.

Surface area of pyramid=(2×s×l)+s2\text{Surface area of pyramid} = (2 \times s \times l) + s^2Surface area of pyramid=(2×s×l)+s2

Step 4, Substitute the values into the formula.

Surface area=(2×75×50)+5625\text{Surface area} = (2 \times 75 \times 50) + 5625Surface area=(2×75×50)+5625 =7500+5625= 7500 + 5625=7500+5625 =13125  sq. ft= 13125\; \text{sq. ft}=13125sq. ft Example 2: Calculating Canvas Area for a Tent Problem:

The base of a square pyramid has dimensions 10  units×10  units10\; \text{units} \times 10\; \text{units}10units×10units and the slant height is 444 units. What is the area of the canvas she will require to build the tent?

Step-by-step solution:

Step 1, Calculate the base area of the tent.

Base area=Area of a square=10×10=100 square units\text{Base area} = \text{Area of a square} = 10 \times 10 = 100 \text{ square units}Base area=Area of a square=10×10=100 square units

Step 2, Note the slant height of the tent is 444 units.

Step 3, Use the surface area formula to find the total canvas needed.

Surface area of pyramid=2×s×l+Base Area\text{Surface area of pyramid} = 2 \times s \times l + \text{Base Area}Surface area of pyramid=2×s×l+Base Area

Step 4, Put the values into the formula.

=(2×10×4)+100= (2 \times 10 \times 4) + 100=(2×10×4)+100 =80+100= 80 + 100=80+100 =180  sq. units= 180\; \text{sq. units}=180sq. units Example 3: Computing Surface Area of a Triangular Pyramid Problem:

For the triangular pyramid, the side length of the base is 777 cm and height of the base is 666 cm. Find its surface area if the slant height of the pyramid is 161616 cm.

Step-by-step solution:

Step 1, Write down the given measurements.

Side length of the base = 777 cm Height of the base = 666 cm Slant height = 1116 cm

Step 2, Use the surface area formula for a triangular pyramid.

Surface area of pyramid = 12×b×h+32×b×l\frac{1}{2} \times b \times h + \frac{3}{2} \times b \times l21​×b×h+23​×b×l Where: bbb = side of the base hhh = height of the base lll = slant height

Step 3, Substitute the values into the formula.

Surface area = (12×7×6)+(32×7×16)(\frac{1}{2} \times 7 \times 6) + (\frac{3}{2} \times 7 \times 16)(21​×7×6)+(23​×7×16)

Step 4, Calculate each part of the formula.

= 21  cm2+168  cm221\; \text{cm}^2 + 168\; \text{cm}^221cm2+168cm2 = 189  cm2189\; \text{cm}^2189cm2 Comments(1)TTrainerWaltNovember 4, 2025I've been struggling to explain pyramid surface area. This page's def and examples are a lifesaver! Great for helping my students grasp it.

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