Question

Kayla used 4 isosceles and one square for her figure. Each edge of the square was 10 inches. The two congruent sides of the triangles are 13 inches long. The height of the triangles is 12 inches. Which figure did kayla construct? What is the surface area of the figure? SHOW YOUR WORK .

Answer 1

Kayla constructed a square pyramid.

The area of the square is 10*10 = 100.

The area of each of the triangles are 12*5/2 = 30.

In total, we get 30*4 + 100 = 220.

Answer 2

Kayla construct square pyramid and its surface area is equals to

340square inches.

What is square pyramid?

" Square pyramid is defined as a three dimensional geometrical shape with square as its base and lateral faces are formed by four triangle joined at a vertex."

Formula used

Surface area of the square pyramid

= Area of the base + Area of the four triangles

Area of the square = (side length)²

Area of the triangle = $\frac{1}{2}$ × base × height

According to the question,

Number of isosceles triangle = 4

Number of square = 1

Side length of the square = 10inches

Height of the triangle = 12inches

Measure of congruent sides of the triangles=13 inches

Substitute the value in the formula we get,

Area of the square $= (10)^{2}$

                                $=100$ square inches.            ____(1)

Here Side of the square is the base of the triangle

Therefore, Base of the triangle = 10inches

Area of the one triangle $= \frac{1}{2} (10)(12)$

                                $=60$ square inches

Area of the four triangles = 60 × 4

                                           = 240 square inches       ____(2)

Substitute the value of (1) and (2) to get the value of ,

surface area of the square pyramid = 100 + 240

                                                             = 340 square inches

Hence, Kayla construct square pyramid and its surface area is equals to

340square inches.

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